Diplomado Econometría Modulo IV: Modelos de Datos de Panel
Universidad Nacional Autónoma de México (UNAM)
Mtro. Diego Sánchez Rojas
Sección 2: Modelos de Datos Panel Estático
2.1 Modelos de efectos fijos
2.2 Modelos de efectos aleatorios
¿Qué son los datos panel ?
Observaciones repetidas en el tiempo de las características de una misma muestra o población.
También conocidos como datos longitudinales o conjuntos de datos de series de tiempo transversales.
Objetivo : Analizar el comportamiento de una variable y los factores que influyen en ésta, durante un período de tiempo determinado.
Ejemplos de Datos Panel (1)
Kessler y Roth (2014) en “Getting More Organs for Transplantation” exploran la relación de como las políticas de consentimiento impactan las tasas de donación de organos.
Ejemplos de Datos Panel (2)
F. Vella and M. Verbeek (1998) en “Whose Wages Do Unions Raise? A Dynamic Model of Unionism and Wage Rate Determination for Young Men” en el Journal of Applied Econometrics
Diseños de Datos Panel
Panel Balanceado
Todos los participantes tienen medición en todos los períodos de tiempo. En este caso el número de observaciones (n) será \(n = NxT\)
Panel No Balanceado
No se tiene observaciones de todos los participantes en todos los períodos de tiempo analizados. Por tanto, \(n \< NxT.\)
Datos Completos
Sin datos faltantas, el conjunto de observaciones planeadas se logró realizar.
Datos Incompletos
Datos faltantes en el panel, el conjunto de observaciones planeadas no se logró colectar.
Estructuras de datos
¿Qué tipo de estructura tienen los datos longitudinales?
Fomarto Wide (Amplio): Cada fila es ocupada por un individuo o entidad y sus variables en el tiempo ocupan un columna de forma individual
Formato Long (Largo): Cada fila es ocupada por un individuo o entidad y sus variables asociadas en un momento específico
Ejemplo en R: Wide a Long 1
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<- reshape (datos_wide, direction = "long" ,varying = list (c ("Estres_0m" , "Estres_3m" , "Estres_6m" ),c ("Sueno_0m" , "Sueno_3m" , "Sueno_6m" )),v.names = c ("Estres" , "Sueno" ),timevar = "Tiempo" ,times = c (0 , 3 , 6 ),idvar = "ID_Participante" ) |> arrange (ID_Participante)print (datos_long)
ID_Participante Tiempo Estres Sueno
1.0 1 0 7 6.5
1.3 1 3 6 7.0
1.6 1 6 5 7.5
2.0 2 0 8 5.5
2.3 2 3 7 6.0
2.6 2 6 6 6.5
3.0 3 0 5 7.0
3.3 3 3 6 6.5
3.6 3 6 4 7.5
Ejemplo en R: Wide a Long 2
Uso de la función pivot_longer()
<- datos_wide |> pivot_longer (cols = matches ("^(Estres|Sueno)_(0m|3m|6m)$" ), # selecciona todas las columnas de interés names_to = c (".value" , "Tiempo" ), # .value = nombre de variable base, Tiempo = medición names_pattern = "^(Estres|Sueno)_(0m|3m|6m)$" # extrae variable y tiempo del nombre de columna |> arrange (ID_Participante)print (datos_long_2)
# A tibble: 9 × 4
ID_Participante Tiempo Estres Sueno
<int> <chr> <dbl> <dbl>
1 1 0m 7 6.5
2 1 3m 6 7
3 1 6m 5 7.5
4 2 0m 8 5.5
5 2 3m 7 6
6 2 6m 6 6.5
7 3 0m 5 7
8 3 3m 6 6.5
9 3 6m 4 7.5
Ejemplo en R: Long a Wide
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<- reshape (datos_long,direction = "wide" ,idvar = "ID_Participante" ,timevar = "Tiempo" ,v.names = c ("Estres" , "Sueno" ))print (datos_wide_n)
ID_Participante Estres.0 Sueno.0 Estres.3 Sueno.3 Estres.6 Sueno.6
1.0 1 7 6.5 6 7.0 5 7.5
2.0 2 8 5.5 7 6.0 6 6.5
3.0 3 5 7.0 6 6.5 4 7.5
Ejemplo en R: Long a Wide 2
Uso de la función pivot_wider()
<- datos_long %>% pivot_wider (id_cols = ID_Participante, # Identifica cada fila base names_from = Tiempo, # Columna que contiene los periodos values_from = c (Estres, Sueno), # Columnas que se expanden a wide names_glue = "{.value}.{Tiempo}" # Controla cómo se construyen los nombres finales print (datos_wide_n_1)
# A tibble: 3 × 7
ID_Participante Estres.0 Estres.3 Estres.6 Sueno.0 Sueno.3 Sueno.6
<int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 1 7 6 5 6.5 7 7.5
2 2 8 7 6 5.5 6 6.5
3 3 5 6 4 7 6.5 7.5
Modelos Lineales con Datos Panel Estáticos
¿Por qué es funcional tener conjuntos de datos panel?
Tener datos en el tiempo de las mismas unidades de corte transversal nos permite analizar de forma dinámica relaciones entre variables.
Controlar la heterogeneidad no observada de corte transversal.
Se puede resolver uno de los problemas principales en la microeconometría e inferencia causal: el problma de la variable omitida
Modelos Lineales con Datos Panel Estáticos
Heterogeneidad
Modelos Lineales con Datos Panel Estáticos
Heterogeneidad
Relaciones entre variables pueden tener grandes diferencias entre los diferentes grupos o subgrupos.
Modelos Lineales con Datos Panel Estáticos
Existen diferencias no observadas (muchas veces no pueden ser observadas) que afectan la variable de interés:
Factores culturales, historia, políticas públicas, geografía, clima, etc.
Si no controlamos, pueden sesgar tus estimaciones.
Este sesgo es el famoso sesgo por variable omitida : confundes el efecto de una variable observada con el de una no observada pero correlacionada.
Intuición:
Relación Esperanza de vidas y PIB percapita: \(\beta\) podría capturar tanto el efecto del PIB como el efecto de factores no observados correlacionados (infraestructura sanitaria, educación, estabilidad política), que además suelen ser similares dentro de cada continente. Por tanto, la estimación estaría sesgada.
Modelos Lineales con Datos Panel Estáticos: Problema de variable omitida
La principal motivación para utilizar datos panel es el problema de la variable omitida
Nos interesa encontrar efectos parciales de un conjunto de variables explicativas en una función de regresión poblacional :
\[ E(y|x_{1}, x_{2}, ... x_{k}, c ) = \textbf{x}\boldsymbol{\beta} + c \]
Donde c es una variable aleatoria que no observamos.
Constante en el tiempo, por tanto tendrá un efecto parcial sobre el tiempo, y como no es es observado le llamaremos efecto no observado .
A nivel individual este tipo de variables son preferencias personales, redes sociales, moral, características como las habilidades cognitivas, la motivación, educación precoz, moral,etc.
Modelos Lineales con Datos Panel Estáticos: Problema de variable omitida
Asumiendo un modelo poblacional:
\[ E(y|\mathbf{x},c ) = \beta_o+ \textbf{x}\boldsymbol{\beta} + c \]
Si \(\mathrm{Cov}(\mathbf{x}, c) \neq 0\)
Variable proxy: \(c\) y usarla en el modelo para reducir el sesgo.
Variables instrumentales (IV): \(x\) pero no con el error \(c\) , estimando con métodos como 2SLS.
Instrumentos con múltiples indicadores:
Modelos Lineales con Datos Panel Estáticos
¿Cómo el uso de datos panel podría resolver el problema de variable omitida?
Aprovechando la información y estructura de datos panel podemos:
Observar cambios dentro de cada unidad a lo largo del tiempo, en lugar de solo diferencias entre unidades.
Controlar las características fijas en el tiempo (cultura, ubicación, instituciones históricas) que no podemos medir pero que podrían sesgar el análisis.
Separar el efecto de las variables que cambian con el tiempo (PIB, gasto en salud) de las que son constantes.
Esto reduce el sesgo porque las comparaciones se hacen contra la propia unidad en el tiempo, no solo entre unidades distintas.
Modelos Lineales con Datos Panel Estáticos
Pooled OLS or POLS (¿Cómo funciona?)
Estimación de OLS con datos longitudinales.
\[ y_{t} = \textbf{x}_{t}\boldsymbol{\beta} + u_{t}~~~t=1,2,3,..., T \]
Donde:
\(y_{t} ~vector~ de~ nT~ \times ~1\)
\(\textbf{x}_{t}~matriz~de~nT\times K\)
\(u_{t}~vector~de~nT\times 1\)
No se toma el diseño de datos panel, es decir la temporalidad y la dimensión transversal.
Modelos Lineales con Datos Panel Estáticos
Para identificar una observación específica usamos subíndices:
\(y_{it}\) = variable para el individuo (o unidad) \(i\) en el tiempo \(t\) .
El modelo puede parecer restrictivo porque el coeficiente \(\beta\) es igual en todos los períodos.
Pero al elegir las variables explicativas \(x_{it}\) correctamente, podemos capturar cambios en los parámetros a lo largo del tiempo. Por ejemplo: una dummy de tiempo que sirva para capturar efectos específicos de cada año.
Es decir, cambios que afectan a todos por igual en ese año, como una crisis económica o un cambio en la ley.
Modelos Lineales con Datos Panel Estáticos: ¿Cómo funciona?
Ecuación de salarios con datos de panel
Tenemos datos para los años 1990, 1991 y 1992 sobre un mismo conjunto de individuos y queremos estimar el efecto del uso de computadoras sobre el salario.
\[\log(wage_{it}) = \beta_0 + \theta_1 d91_t + \theta_2 d92_t
+ \delta_1 computer_{it} + \delta_2 educ_{it}
+ \delta_3 exper_{it} + \delta_4 female_i + u_{it}\]
Donde:
\(d91_t, d92_t\) : dummies para 1991 y 1992 (efectos de tiempo).\(computer_{it}\) : uso de computadora por persona (i) en año (t).\(educ_{it}\) : años de educación (puede variar en el tiempo para algunos).\(exper_{it}\) : experiencia laboral.\(female_i\) : dummy de género (constante en el tiempo).
Modelos Lineales con Datos Panel Estáticos: ¿Cómo funciona?
Constantes en el tiempo : \(female_i\) , industria.
Cambiantes en el tiempo : uso de computadora, experiencia, educación.
Aunque el coeficiente \(\delta\) es fijo para otras variables, los coeficientes \(\theta_1\) y \(\theta_2\) asociados a las dummies permiten capturar efectos distintos en cada año, es decir, permiten que el modelo refleje cambios en el impacto del tiempo.
Modelos Lineales con Datos Panel Estáticos: POLS (Supuestos)
Supuestos
POLS1. Exogeneidad (Media cero de los errores)\[E( \textbf{x}_{t}' u_{t}) = 0~~~t=1,2,..., T\]
POLS2. No multicolinealidad (no combinación lineal exacta)\[rank[\sum_{t=1}^{T}E(\textbf{x}_{t}'\textbf{x}_{t})] = K\]
Si el rango es igual a K (el número de variables explicativas), significa que todas las variables son linealmente independientes entre sí.
Por lo tanto, no hay ninguna variable que pueda escribirse exactamente como combinación lineal de otras variables.
Modelos Lineales con Datos Panel Estáticos: POLS (Supuestos)
Modelos Lineales con Datos Panel Estáticos: POLS (Implementación)
Modelo de efectos no observados a estimar por POLS :
\[ y_{it}= \textbf{x}_{it}\boldsymbol{\beta} + c_{i}+ u_{it} ~~~t=1,2,...T\]
Donde tendrá un error compuesto que será la suma del error no observado (efecto no observado) y un error idiosincrático
\[ v_{it } = c_{i}+ u_{it} ~~~t=1,2,...T\]
Modelos Lineales con Datos Panel Estáticos: POLS (Implementación)
No olvidemos
\(c_i\) Efecto no observado
Características constantes en el tiempo para cada unidad (i).
No se miden directamente.
Ejemplos:
Personas: habilidades innatas, entorno familiar.
Empresas: ubicación, cultura organizacional.
\(u_{it}\) Error idiosincrático
Factores que cambian con el tiempo y afectan solo esa observación.
Ejemplos:
Personas: enfermedad puntual, aumento temporal de productividad.
Empresas: fluctuación de demanda, problemas temporales
Modelos Lineales con Datos Panel Estáticos: POLS (Implementación)
La estimación por Pooled OLS or POLS del MEO será consistente si se cumple principalmente que:
\[ E( \textbf{x}_{it}' v_{it}) = 0~~~t=1,2,..., T\]
Se tiene que cumplir que:
\[ E( \textbf{x}_{it}' u_{it}) = 0 ~~~~~y~~~ E( \textbf{x}_{it}' c_{i}) = 0~~~t=1,2,..., T\]
Modelos Lineales con Datos Panel Estáticos: POLS (Implementación)
POLS3.
No correlación serial
\[E(v_{it}v_{is}\textbf{x}_{it}'\textbf{x}_{is}) = 0~~~~~, t\neq s~~~t,s=1,2,...t\]
\[ E(v_{it}v_{is})=0\]
Modelos Lineales con Datos Panel Estáticos: POLS (Consideraciones)
Pooled OLS estima el modelo de panel como si todos los datos fueran una sola gran muestra de corte transversal.
No diferencia entre variación entre individuos y a lo largo del tiempo .
Como \(v_{it} = c_i + u_{it}\) y \(c_i\) es constante en el tiempo, existe correlación perfecta entre \(v_{it}\) y \(v_{is}\) para un mismo individuo
Por eso, en la práctica POLS no es consistente si \(x_{it}\) está correlacionada con \(c_i\)
Para que POLS sea aplicable y consistente necesitamos:
Modelos Lineales con Datos Panel Estáticos: POLS (Implementación en R)
install.packages ('pacman' )library ('pacman' )p_load ('causaldata' ,'plm' , 'modelsummary' )data ("gapminder" , package = "causaldata" )head (gapminder)
# A tibble: 6 × 6
country continent year lifeExp pop gdpPercap
<fct> <fct> <int> <dbl> <int> <dbl>
1 Afghanistan Asia 1952 28.8 8425333 779.
2 Afghanistan Asia 1957 30.3 9240934 821.
3 Afghanistan Asia 1962 32.0 10267083 853.
4 Afghanistan Asia 1967 34.0 11537966 836.
5 Afghanistan Asia 1972 36.1 13079460 740.
6 Afghanistan Asia 1977 38.4 14880372 786.
Modelos Lineales con Datos Panel Estáticos
Pooled OLS or POLS (Implementación en R)
Objeto clase pdata.frame() es un data.frame con un índice que describe sus dimensiones individual y temporal.
<- pdata.frame (gapminder, index = c ("country" , "year" ))head (df_paneld)
country continent year lifeExp pop gdpPercap
Afghanistan-1952 Afghanistan Asia 1952 28.801 8425333 779.4453
Afghanistan-1957 Afghanistan Asia 1957 30.332 9240934 820.8530
Afghanistan-1962 Afghanistan Asia 1962 31.997 10267083 853.1007
Afghanistan-1967 Afghanistan Asia 1967 34.020 11537966 836.1971
Afghanistan-1972 Afghanistan Asia 1972 36.088 13079460 739.9811
Afghanistan-1977 Afghanistan Asia 1977 38.438 14880372 786.1134
Modelos Lineales con Datos Panel Estáticos
Pooled OLS or POLS (Implementación en R)
Estimamos modelo Pooled OLS con la función plm():
# Estimación de modelos: Pooled OLS <- plm (lifeExp ~ log (gdpPercap) , data = df_paneld, model = 'pooling' )summary (pooled_plm)
Pooling Model
Call:
plm(formula = lifeExp ~ log(gdpPercap), data = df_paneld, model = "pooling")
Balanced Panel: n = 142, T = 12, N = 1704
Residuals:
Min. 1st Qu. Median 3rd Qu. Max.
-32.7778 -4.2042 1.2124 4.6576 19.2849
Coefficients:
Estimate Std. Error t-value Pr(>|t|)
(Intercept) -9.10089 1.22767 -7.4131 1.935e-13 ***
log(gdpPercap) 8.40508 0.14876 56.5002 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Total Sum of Squares: 284150
Residual Sum of Squares: 98814
R-Squared: 0.65225
Adj. R-Squared: 0.65204
F-statistic: 3192.27 on 1 and 1702 DF, p-value: < 2.22e-16
Modelos Lineales con Datos Panel Estáticos POLS (Implementación en R)
Estimamos el modelo Pooled OLS con la función lm()
Interpretación: El coeficiente del log(gdpPercap) indica que un aumento del 1% en el PIB per cápita está asociado con un aumento de 0.0840 años (alrededor de 30.7 días) en la esperanza de vida.
# Estimación de modelos: Pooled OLS <- lm (lifeExp ~ log (gdpPercap) , data = df_paneld)summary (pooled_lm)
Call:
lm(formula = lifeExp ~ log(gdpPercap), data = df_paneld)
Residuals:
Min 1Q Median 3Q Max
-32.778 -4.204 1.212 4.658 19.285
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -9.1009 1.2277 -7.413 1.93e-13 ***
log(gdpPercap) 8.4051 0.1488 56.500 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 7.62 on 1702 degrees of freedom
Multiple R-squared: 0.6522, Adjusted R-squared: 0.652
F-statistic: 3192 on 1 and 1702 DF, p-value: < 2.2e-16
Modelos Lineales con Datos Panel Estáticos Pooled OLS or POLS (Implementación en R 2)
F. Vella and M. Verbeek (1998), “Whose Wages Do Unions Raise? A Dynamic Model of Unionism and Wage Rate Determination for Young Men”
Ecuación de salario a estimar es:
\[lwage_{it} = \beta_0 + \beta_1 union_{it} + \beta_2 educ_{it} + \beta_3 exper_{it} + \beta_4 exper_{it}^2 + u_{it} \]
\(lwage\) : Logaritmo natural del salario (variable dependiente)
\(union\) : Variable dummy que indica si el trabajador pertenece a un sindicato (1 = sí, 0 = no)
\(educ\) : Años de educación del trabajador
\(exper\) : Años de experiencia laboral
\(exper^2\) : Años de experiencia laboral al cuadrado
Coeficiente objetivo: \(\beta_1\)
Modelos Lineales con Datos Panel Estáticos Pooled OLS or POLS (Implementación en R 2)
En R podemos encontrar el conjunto de datos en wooldridge como wagepan:
p_load ('wooldridge' , 'plm' )#Cargamos datos data ("wagepan" )#utilizamos plm para darle estructura de panel <- pdata.frame (wagepan, index = c ("nr" , "year" ))print (pdata_wage)
nr year agric black bus construc ent exper fin hisp poorhlth hours
13-1980 13 1980 0 0 1 0 0 1 0 0 0 2672
13-1981 13 1981 0 0 0 0 0 2 0 0 0 2320
13-1982 13 1982 0 0 1 0 0 3 0 0 0 2940
13-1983 13 1983 0 0 1 0 0 4 0 0 0 2960
13-1984 13 1984 0 0 0 0 0 5 0 0 0 3071
13-1985 13 1985 0 0 1 0 0 6 0 0 0 2864
13-1986 13 1986 0 0 1 0 0 7 0 0 0 2994
13-1987 13 1987 0 0 1 0 0 8 0 0 0 2640
17-1980 17 1980 0 0 0 0 0 4 0 0 0 2484
17-1981 17 1981 0 0 0 0 0 5 0 0 0 2804
17-1982 17 1982 0 0 0 0 0 6 0 0 0 2530
17-1983 17 1983 0 0 0 0 0 7 0 0 0 2340
17-1984 17 1984 0 0 0 0 0 8 0 0 0 2486
17-1985 17 1985 0 0 0 1 0 9 0 0 0 2164
17-1986 17 1986 0 0 0 1 0 10 0 0 0 2749
17-1987 17 1987 0 0 0 1 0 11 0 0 0 2476
18-1980 18 1980 0 0 0 0 0 4 0 0 0 2332
18-1981 18 1981 0 0 0 0 0 5 0 0 0 2116
18-1982 18 1982 0 0 0 0 0 6 0 0 0 2500
18-1983 18 1983 0 0 0 0 0 7 0 0 0 2474
18-1984 18 1984 0 0 0 0 0 8 0 0 0 2362
18-1985 18 1985 0 0 0 0 0 9 0 0 0 2340
18-1986 18 1986 0 0 0 0 0 10 0 0 0 2340
18-1987 18 1987 0 0 0 0 0 11 0 0 0 2340
45-1980 45 1980 0 0 0 0 0 2 0 0 0 1864
45-1981 45 1981 0 0 0 0 0 3 0 0 0 2021
45-1982 45 1982 0 0 0 0 0 4 0 0 0 2274
45-1983 45 1983 0 0 0 0 0 5 0 0 0 2112
45-1984 45 1984 0 0 1 0 0 6 0 0 0 1920
45-1985 45 1985 0 0 0 0 0 7 0 0 0 2205
45-1986 45 1986 0 0 0 0 0 8 0 0 0 2551
45-1987 45 1987 0 0 0 1 0 9 0 0 0 2860
110-1980 110 1980 0 0 0 0 0 5 0 0 0 2080
110-1981 110 1981 0 0 0 0 0 6 0 0 0 2080
110-1982 110 1982 0 0 0 0 0 7 0 0 0 2639
110-1983 110 1983 0 0 0 0 0 8 0 0 0 2223
110-1984 110 1984 0 0 0 0 0 9 0 0 0 2150
110-1985 110 1985 0 0 1 0 0 10 0 0 0 1532
110-1986 110 1986 0 0 0 0 0 11 1 0 0 2080
110-1987 110 1987 0 0 0 0 0 12 1 0 0 2080
120-1980 120 1980 0 0 0 0 0 2 0 0 0 1025
120-1981 120 1981 0 0 0 0 0 3 0 0 0 1496
120-1982 120 1982 0 0 0 0 0 4 0 0 0 1394
120-1983 120 1983 0 0 0 0 0 5 0 0 0 2924
120-1984 120 1984 0 0 0 0 1 6 0 0 0 3564
120-1985 120 1985 0 0 0 0 0 7 0 0 0 3979
120-1986 120 1986 0 0 0 0 0 8 1 0 0 4351
120-1987 120 1987 0 0 1 0 0 9 0 0 0 3568
126-1980 126 1980 0 0 0 0 0 2 0 0 0 3115
126-1981 126 1981 0 0 0 0 0 3 0 0 0 2735
126-1982 126 1982 0 0 0 0 0 4 0 0 0 2390
126-1983 126 1983 0 0 0 0 0 5 0 0 0 2340
126-1984 126 1984 0 0 0 0 0 6 0 0 0 2250
126-1985 126 1985 0 0 0 0 0 7 0 0 0 2340
126-1986 126 1986 0 0 0 0 0 8 0 0 0 2941
126-1987 126 1987 0 0 0 0 0 9 0 0 0 2847
150-1980 150 1980 0 0 1 0 0 2 0 0 0 1876
150-1981 150 1981 0 0 1 0 0 3 0 0 0 2327
150-1982 150 1982 0 0 1 0 0 4 0 0 0 2006
150-1983 150 1983 0 0 1 0 0 5 0 0 0 1826
150-1984 150 1984 0 0 1 0 0 6 0 0 0 3414
150-1985 150 1985 0 0 1 0 0 7 0 0 0 3928
150-1986 150 1986 0 0 1 0 0 8 0 0 0 4000
150-1987 150 1987 0 0 1 0 0 9 0 0 0 4992
162-1980 162 1980 0 0 0 0 0 2 0 0 0 1874
162-1981 162 1981 0 0 0 0 0 3 0 0 0 1710
162-1982 162 1982 0 0 0 0 0 4 0 0 0 1488
162-1983 162 1983 0 0 0 0 0 5 0 0 0 939
162-1984 162 1984 0 0 0 0 0 6 0 0 0 1980
162-1985 162 1985 0 0 0 0 0 7 0 0 0 2735
162-1986 162 1986 0 0 0 0 0 8 0 0 0 2720
162-1987 162 1987 0 0 0 0 0 9 0 0 0 2795
166-1980 166 1980 0 0 0 0 0 2 0 0 0 1296
166-1981 166 1981 0 0 0 0 0 3 0 0 0 1942
166-1982 166 1982 0 0 0 0 0 4 0 0 0 1245
166-1983 166 1983 0 0 0 0 0 5 0 0 0 1196
166-1984 166 1984 0 0 0 0 0 6 0 0 0 2387
166-1985 166 1985 0 0 0 0 0 7 0 0 0 2160
166-1986 166 1986 0 0 0 0 0 8 0 0 0 2336
166-1987 166 1987 0 0 0 0 0 9 0 0 0 2301
189-1980 189 1980 0 0 0 0 0 2 0 0 0 520
189-1981 189 1981 0 0 0 0 0 3 0 0 0 520
189-1982 189 1982 0 0 0 0 0 4 0 0 0 520
189-1983 189 1983 0 0 0 0 0 5 0 0 0 520
189-1984 189 1984 0 0 0 0 0 6 0 0 0 1400
189-1985 189 1985 0 0 0 0 0 7 0 0 0 1754
189-1986 189 1986 0 0 0 0 0 8 0 0 0 1840
189-1987 189 1987 0 0 0 0 0 9 0 0 0 1872
193-1980 193 1980 0 0 0 0 0 2 0 0 0 980
193-1981 193 1981 0 0 0 0 0 3 0 0 0 925
193-1982 193 1982 0 0 0 0 0 4 0 0 0 2187
193-1983 193 1983 0 0 0 0 0 5 0 0 0 2080
193-1984 193 1984 0 0 0 0 0 6 0 0 0 2346
193-1985 193 1985 0 0 0 0 0 7 0 0 0 2487
193-1986 193 1986 0 0 0 0 0 8 0 0 0 2328
193-1987 193 1987 0 0 0 0 0 9 0 0 0 2132
209-1980 209 1980 0 0 0 0 0 3 0 0 0 2340
209-1981 209 1981 0 0 0 0 0 4 0 0 0 1935
209-1982 209 1982 0 0 0 0 0 5 0 0 0 2080
209-1983 209 1983 0 0 0 0 0 6 0 0 0 2080
209-1984 209 1984 0 0 0 0 1 7 0 0 0 2280
209-1985 209 1985 0 0 0 0 0 8 0 0 0 2520
209-1986 209 1986 0 0 0 0 0 9 0 0 0 2395
209-1987 209 1987 0 0 0 0 1 10 0 0 0 2145
212-1980 212 1980 0 0 0 0 0 2 0 0 0 2080
212-1981 212 1981 0 0 0 0 0 3 0 0 0 2080
212-1982 212 1982 0 0 0 0 0 4 0 0 0 2110
212-1983 212 1983 0 0 0 0 0 5 0 0 0 2550
212-1984 212 1984 0 0 0 0 0 6 0 0 0 2560
212-1985 212 1985 0 0 0 0 0 7 0 0 0 2704
212-1986 212 1986 0 0 0 0 0 8 0 0 0 2856
212-1987 212 1987 0 0 0 0 0 9 0 0 0 2912
218-1980 218 1980 0 0 0 0 0 2 0 0 0 2080
218-1981 218 1981 0 0 0 0 0 3 0 0 0 2530
218-1982 218 1982 0 0 0 0 0 4 0 0 0 2240
218-1983 218 1983 0 0 1 0 0 5 0 0 0 2520
218-1984 218 1984 0 0 0 0 0 6 0 0 0 2405
218-1985 218 1985 0 0 1 0 0 7 0 0 0 2130
218-1986 218 1986 0 0 1 0 0 8 0 0 0 2080
218-1987 218 1987 0 0 1 0 0 9 0 0 0 2080
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1142-1983 1142 1983 0 0 0 0 0 5 0 1 0 2175
1142-1984 1142 1984 0 0 0 0 0 6 1 1 0 2340
1142-1985 1142 1985 0 0 0 0 0 7 1 1 0 2340
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1142-1987 1142 1987 0 0 0 0 0 9 1 1 0 2451
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1156-1983 1156 1983 0 1 0 0 0 8 0 0 0 2000
1156-1984 1156 1984 0 1 0 0 0 9 0 0 0 1730
1156-1985 1156 1985 0 1 0 0 0 10 0 0 0 1820
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1156-1987 1156 1987 0 1 0 0 0 12 0 0 0 1750
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1180-1984 1180 1984 0 0 0 1 0 6 0 0 0 2180
1180-1985 1180 1985 0 0 0 1 0 7 0 0 0 2080
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1180-1987 1180 1987 0 0 0 1 0 9 0 0 0 2080
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1190-1981 1190 1981 0 1 0 0 0 3 0 0 0 1960
1190-1982 1190 1982 0 1 0 0 0 4 0 0 0 2080
1190-1983 1190 1983 0 1 0 0 0 5 0 0 0 2080
1190-1984 1190 1984 0 1 0 0 0 6 0 0 0 2280
1190-1985 1190 1985 1 1 0 0 0 7 0 0 0 1880
1190-1986 1190 1986 0 1 0 0 0 8 0 0 0 2080
1190-1987 1190 1987 0 1 0 0 0 9 0 0 0 2080
1204-1980 1204 1980 0 0 0 0 0 5 0 0 0 2160
1204-1981 1204 1981 0 0 0 0 0 6 0 0 0 2080
1204-1982 1204 1982 0 0 0 0 0 7 0 0 0 2080
1204-1983 1204 1983 0 0 0 0 0 8 0 0 0 2080
1204-1984 1204 1984 0 0 0 0 0 9 0 0 0 2080
1204-1985 1204 1985 0 0 0 0 0 10 0 0 0 2080
1204-1986 1204 1986 0 0 0 0 0 11 0 0 0 2080
1204-1987 1204 1987 0 0 0 0 0 12 0 0 0 2080
1249-1980 1249 1980 0 0 0 0 0 5 0 0 0 2585
1249-1981 1249 1981 0 0 0 0 0 6 0 0 0 3050
1249-1982 1249 1982 1 0 0 0 0 7 0 0 0 2460
1249-1983 1249 1983 1 0 0 0 0 8 0 0 0 2800
1249-1984 1249 1984 1 0 0 0 0 9 0 0 1 3085
1249-1985 1249 1985 0 0 0 0 0 10 0 0 0 2925
1249-1986 1249 1986 0 0 0 0 0 11 0 0 0 2188
1249-1987 1249 1987 0 0 0 0 0 12 0 0 0 2404
1272-1980 1272 1980 0 0 0 0 0 3 0 0 0 1560
1272-1981 1272 1981 0 0 0 0 0 4 0 0 0 1560
1272-1982 1272 1982 0 0 0 0 0 5 0 0 0 1560
1272-1983 1272 1983 0 0 0 0 0 6 0 0 1 1560
1272-1984 1272 1984 0 0 0 0 0 7 0 0 0 2020
1272-1985 1272 1985 0 0 0 0 0 8 0 0 0 2203
1272-1986 1272 1986 0 0 0 0 0 9 0 0 0 2104
1272-1987 1272 1987 0 0 0 0 0 10 0 0 0 2080
1311-1980 1311 1980 0 0 0 0 0 2 0 0 0 4057
1311-1981 1311 1981 0 0 0 0 0 3 0 0 0 4732
1311-1982 1311 1982 0 0 0 0 0 4 0 0 0 4732
1311-1983 1311 1983 0 0 0 0 0 5 0 0 0 4932
1311-1984 1311 1984 0 0 0 0 0 6 0 0 0 3060
1311-1985 1311 1985 0 0 0 0 0 7 0 0 0 3860
1311-1986 1311 1986 0 0 0 0 0 8 0 0 0 4418
1311-1987 1311 1987 0 0 0 0 0 9 0 0 0 2845
1316-1980 1316 1980 0 0 1 0 0 4 0 0 0 2080
1316-1981 1316 1981 0 0 0 1 0 5 0 0 0 1920
1316-1982 1316 1982 0 0 0 0 0 6 0 0 0 1840
1316-1983 1316 1983 0 0 0 0 0 7 0 0 0 2055
1316-1984 1316 1984 0 0 0 0 0 8 0 0 0 2080
1316-1985 1316 1985 0 0 0 1 0 9 0 0 0 2310
1316-1986 1316 1986 0 0 0 1 0 10 0 0 0 2155
1316-1987 1316 1987 0 0 0 0 0 11 0 0 0 2080
1318-1980 1318 1980 0 0 0 1 0 8 0 0 0 1840
1318-1981 1318 1981 1 0 0 0 0 9 0 0 0 2028
1318-1982 1318 1982 1 0 0 0 0 10 0 0 0 2560
1318-1983 1318 1983 1 0 0 0 0 11 0 0 0 2600
1318-1984 1318 1984 0 0 0 0 0 12 0 0 0 2600
1318-1985 1318 1985 1 0 0 0 0 13 0 0 0 2318
1318-1986 1318 1986 0 0 0 0 0 14 0 0 0 2288
1318-1987 1318 1987 1 0 0 0 0 15 0 0 0 2288
1345-1980 1345 1980 0 0 0 0 0 4 0 0 0 1970
1345-1981 1345 1981 0 0 0 0 0 5 0 0 0 2310
1345-1982 1345 1982 0 0 0 0 0 6 0 0 0 2145
1345-1983 1345 1983 0 0 0 0 0 7 0 0 0 2080
1345-1984 1345 1984 0 0 0 0 0 8 0 0 0 2310
1345-1985 1345 1985 0 0 0 0 0 9 0 0 0 2340
1345-1986 1345 1986 0 0 0 0 0 10 0 0 0 2155
1345-1987 1345 1987 0 0 0 0 0 11 0 0 0 3790
1397-1980 1397 1980 0 0 0 0 0 5 0 0 0 2080
1397-1981 1397 1981 0 0 0 0 0 6 0 0 0 2080
1397-1982 1397 1982 0 0 0 0 0 7 0 0 0 2080
1397-1983 1397 1983 0 0 0 0 0 8 0 0 0 2080
1397-1984 1397 1984 0 0 0 0 0 9 0 0 0 2080
1397-1985 1397 1985 0 0 0 0 0 10 0 0 0 2080
1397-1986 1397 1986 0 0 0 0 0 11 0 0 0 2080
1397-1987 1397 1987 0 0 0 0 0 12 0 0 0 2080
1434-1980 1434 1980 0 0 0 1 0 2 0 0 0 2880
1434-1981 1434 1981 0 0 0 1 0 3 0 0 0 2086
1434-1982 1434 1982 0 0 0 0 0 4 0 0 0 2284
1434-1983 1434 1983 0 0 0 0 0 5 0 0 0 2080
1434-1984 1434 1984 0 0 0 0 1 6 0 0 0 3028
1434-1985 1434 1985 0 0 0 0 0 7 0 0 0 2640
1434-1986 1434 1986 0 0 1 0 0 8 0 0 0 2080
1434-1987 1434 1987 0 0 0 0 0 9 0 0 0 2820
1492-1980 1492 1980 0 0 0 0 0 4 0 0 0 1328
1492-1981 1492 1981 0 0 0 0 0 5 0 0 0 2042
1492-1982 1492 1982 0 0 0 0 0 6 0 0 0 2008
1492-1983 1492 1983 0 0 0 0 0 7 0 0 0 2090
1492-1984 1492 1984 0 0 0 0 0 8 0 0 1 2080
1492-1985 1492 1985 0 0 0 0 0 9 0 0 0 2295
1492-1986 1492 1986 0 0 0 0 0 10 0 0 0 2220
1492-1987 1492 1987 0 0 0 0 0 11 0 0 0 2272
1496-1980 1496 1980 0 0 0 0 0 1 0 0 0 1144
1496-1981 1496 1981 0 0 0 0 0 2 0 0 0 1184
1496-1982 1496 1982 0 0 0 0 0 3 0 0 0 3432
1496-1983 1496 1983 0 0 0 0 0 4 0 0 0 3850
1496-1984 1496 1984 0 0 0 0 0 5 0 0 0 3470
1496-1985 1496 1985 0 0 0 0 0 6 0 0 0 3229
1496-1986 1496 1986 0 0 0 0 0 7 0 0 0 3773
1496-1987 1496 1987 0 0 0 0 0 8 0 0 0 2685
1506-1980 1506 1980 0 0 1 0 0 3 0 0 0 1670
1506-1981 1506 1981 0 0 0 0 0 4 0 0 0 782
1506-1982 1506 1982 0 0 0 0 0 5 0 0 0 2487
1506-1983 1506 1983 0 0 0 0 0 6 0 0 0 2328
1506-1984 1506 1984 0 0 0 0 0 7 0 0 0 2540
1506-1985 1506 1985 0 0 0 0 0 8 0 0 0 2080
1506-1986 1506 1986 0 0 0 0 0 9 0 0 0 2065
1506-1987 1506 1987 0 0 1 0 0 10 0 0 0 3088
1515-1980 1515 1980 0 0 0 0 0 2 0 0 0 2455
1515-1981 1515 1981 0 0 0 0 0 3 0 0 0 2340
1515-1982 1515 1982 0 0 0 0 0 4 0 0 0 2155
1515-1983 1515 1983 0 0 0 0 0 5 0 0 0 2489
1515-1984 1515 1984 0 0 0 0 0 6 0 0 0 2020
1515-1985 1515 1985 0 0 0 0 0 7 0 0 0 2080
1515-1986 1515 1986 0 0 0 0 0 8 0 0 0 2080
1515-1987 1515 1987 0 0 0 0 0 9 0 0 0 2500
1520-1980 1520 1980 0 1 0 0 0 5 0 0 0 2459
1520-1981 1520 1981 1 1 0 0 0 6 0 0 0 2479
1520-1982 1520 1982 1 1 0 0 0 7 0 0 0 2496
1520-1983 1520 1983 0 1 0 0 0 8 0 0 0 2457
1520-1984 1520 1984 0 1 0 0 0 9 0 0 0 2487
1520-1985 1520 1985 0 1 0 0 0 10 0 0 0 2496
1520-1986 1520 1986 0 1 0 0 0 11 0 0 0 2454
1520-1987 1520 1987 0 1 0 0 0 12 0 0 0 2481
1528-1980 1528 1980 0 1 0 0 0 4 0 0 0 1995
1528-1981 1528 1981 0 1 0 0 0 5 0 0 0 2080
1528-1982 1528 1982 0 1 0 0 0 6 0 0 0 2080
1528-1983 1528 1983 0 1 0 0 0 7 0 0 0 2080
1528-1984 1528 1984 0 1 0 0 0 8 0 0 0 1480
1528-1985 1528 1985 0 1 0 0 0 9 0 0 0 1996
1528-1986 1528 1986 0 1 0 0 0 10 0 0 0 1520
1528-1987 1528 1987 0 1 0 0 0 11 0 0 0 2360
1554-1980 1554 1980 0 0 0 0 0 2 0 0 0 2145
1554-1981 1554 1981 0 0 0 0 0 3 0 0 0 2120
1554-1982 1554 1982 0 0 0 0 0 4 0 0 0 2152
1554-1983 1554 1983 0 0 0 0 0 5 0 0 0 2268
1554-1984 1554 1984 0 0 0 0 0 6 0 0 0 2120
1554-1985 1554 1985 0 0 0 0 0 7 0 0 0 2280
1554-1986 1554 1986 0 0 0 0 0 8 0 0 0 2135
1554-1987 1554 1987 0 0 0 0 0 9 0 0 0 3060
1575-1980 1575 1980 0 0 0 0 0 3 1 0 0 2196
1575-1981 1575 1981 0 0 0 0 0 4 1 0 0 2102
1575-1982 1575 1982 0 0 0 0 0 5 1 0 0 2285
1575-1983 1575 1983 0 0 0 0 0 6 1 0 0 2135
1575-1984 1575 1984 0 0 0 0 0 7 1 0 0 3603
1575-1985 1575 1985 0 0 0 0 0 8 1 0 0 2840
1575-1986 1575 1986 0 0 0 0 0 9 1 0 0 3360
1575-1987 1575 1987 0 0 0 0 0 10 1 0 0 3465
1576-1980 1576 1980 0 0 0 0 0 2 0 0 0 2000
1576-1981 1576 1981 0 0 0 0 0 3 1 0 0 2080
1576-1982 1576 1982 0 0 0 0 0 4 0 0 0 2080
1576-1983 1576 1983 0 0 0 0 0 5 0 0 0 2230
1576-1984 1576 1984 0 0 0 1 0 6 0 0 0 2225
1576-1985 1576 1985 0 0 0 1 0 7 0 0 0 2290
1576-1986 1576 1986 0 0 0 1 0 8 0 0 0 2030
1576-1987 1576 1987 0 0 0 1 0 9 0 0 0 2215
1628-1980 1628 1980 0 0 0 0 0 3 0 0 0 2456
1628-1981 1628 1981 0 0 0 0 0 4 0 0 0 2128
1628-1982 1628 1982 0 0 0 0 0 5 0 0 0 1136
1628-1983 1628 1983 0 0 0 0 0 6 0 0 0 2048
1628-1984 1628 1984 0 0 0 0 0 7 0 0 0 2080
1628-1985 1628 1985 0 0 0 0 0 8 0 0 0 2080
1628-1986 1628 1986 0 0 0 0 0 9 0 0 0 2080
1628-1987 1628 1987 0 0 0 0 0 10 0 0 0 2080
1641-1980 1641 1980 0 0 0 0 0 4 0 1 0 2260
1641-1981 1641 1981 0 0 0 0 0 5 0 1 0 2191
1641-1982 1641 1982 0 0 0 0 0 6 0 1 0 2223
1641-1983 1641 1983 0 0 0 0 0 7 0 1 0 2196
1641-1984 1641 1984 0 0 0 0 0 8 0 1 0 2272
1641-1985 1641 1985 0 0 0 0 0 9 0 1 0 2288
1641-1986 1641 1986 0 0 0 0 0 10 0 1 0 1213
1641-1987 1641 1987 0 0 0 0 0 11 1 1 0 2250
1644-1980 1644 1980 0 0 0 0 1 1 0 1 0 1515
1644-1981 1644 1981 0 0 0 0 0 2 1 1 0 2045
1644-1982 1644 1982 0 0 0 0 0 3 1 1 0 2080
1644-1983 1644 1983 0 0 0 0 0 4 1 1 0 2080
1644-1984 1644 1984 0 0 0 0 0 5 1 1 0 2080
1644-1985 1644 1985 0 0 0 0 0 6 1 1 0 2080
1644-1986 1644 1986 0 0 0 0 0 7 1 1 0 2490
1644-1987 1644 1987 0 0 0 0 0 8 1 1 0 2415
1653-1980 1653 1980 0 0 0 0 0 2 0 0 0 1950
1653-1981 1653 1981 0 0 0 0 0 3 0 0 0 1820
1653-1982 1653 1982 0 0 0 0 0 4 0 0 0 2164
1653-1983 1653 1983 0 0 0 0 0 5 0 0 0 2068
1653-1984 1653 1984 0 0 0 0 0 6 0 0 0 2187
1653-1985 1653 1985 0 0 0 0 0 7 1 0 0 2810
1653-1986 1653 1986 0 0 0 0 0 8 1 0 0 2860
1653-1987 1653 1987 0 0 0 0 0 9 1 0 0 2730
1654-1980 1654 1980 0 0 0 0 0 4 0 0 0 2074
1654-1981 1654 1981 0 0 0 0 0 5 0 0 1 2144
1654-1982 1654 1982 0 0 0 1 0 6 0 0 0 1080
1654-1983 1654 1983 0 0 0 0 0 7 0 0 0 1800
1654-1984 1654 1984 0 0 0 0 0 8 0 0 0 2080
1654-1985 1654 1985 0 0 0 0 0 9 0 0 0 2080
1654-1986 1654 1986 0 0 0 0 0 10 0 0 0 2080
1654-1987 1654 1987 0 0 0 0 0 11 0 0 0 2080
1721-1980 1721 1980 0 0 0 0 0 5 0 1 0 2080
1721-1981 1721 1981 0 0 0 0 0 6 0 1 0 2080
1721-1982 1721 1982 0 0 0 0 0 7 0 1 0 2080
1721-1983 1721 1983 0 0 0 0 0 8 0 1 0 2080
1721-1984 1721 1984 0 0 0 0 0 9 0 1 0 2080
1721-1985 1721 1985 0 0 0 0 0 10 0 1 0 2080
1721-1986 1721 1986 0 0 0 0 0 11 0 1 0 2080
1721-1987 1721 1987 0 0 1 0 0 12 0 1 0 2080
1742-1980 1742 1980 0 0 0 0 0 2 0 0 0 2770
1742-1981 1742 1981 0 0 0 0 0 3 0 0 0 2230
1742-1982 1742 1982 0 0 1 0 0 4 0 0 0 2080
1742-1983 1742 1983 0 0 0 0 0 5 0 0 0 2080
1742-1984 1742 1984 0 0 0 0 0 6 0 0 0 2000
1742-1985 1742 1985 0 0 0 0 0 7 0 0 0 2080
1742-1986 1742 1986 0 0 0 0 0 8 0 0 0 2080
1742-1987 1742 1987 0 0 1 0 0 9 0 0 0 1920
1744-1980 1744 1980 0 0 0 1 0 2 0 0 0 2080
1744-1981 1744 1981 0 0 0 1 0 3 0 0 0 2080
1744-1982 1744 1982 0 0 0 1 0 4 0 0 0 1520
1744-1983 1744 1983 0 0 0 1 0 5 0 0 0 1100
1744-1984 1744 1984 0 0 0 0 0 6 0 0 0 1285
1744-1985 1744 1985 0 0 0 0 0 7 0 0 0 1989
1744-1986 1744 1986 0 0 0 1 0 8 0 0 0 2036
1744-1987 1744 1987 0 0 0 1 0 9 0 0 0 1690
1763-1980 1763 1980 0 0 0 0 0 1 0 1 0 1860
1763-1981 1763 1981 0 0 0 0 0 2 0 1 0 1760
1763-1982 1763 1982 0 0 0 0 0 3 0 1 0 1800
1763-1983 1763 1983 0 0 0 0 0 4 0 1 0 1536
1763-1984 1763 1984 0 0 0 0 0 5 0 1 0 1064
1763-1985 1763 1985 0 0 0 0 0 6 0 1 0 760
1763-1986 1763 1986 0 0 0 0 0 7 0 1 1 2164
1763-1987 1763 1987 0 0 0 0 0 8 0 1 0 1296
1777-1980 1777 1980 0 0 0 0 0 1 0 0 0 1985
1777-1981 1777 1981 0 0 0 0 0 2 0 0 0 2080
1777-1982 1777 1982 0 0 0 0 0 3 0 0 0 2665
1777-1983 1777 1983 0 0 0 0 0 4 0 0 0 2790
1777-1984 1777 1984 0 0 0 0 0 5 0 0 0 2540
1777-1985 1777 1985 0 0 0 0 0 6 0 0 0 2600
1777-1986 1777 1986 0 0 0 0 0 7 0 0 0 2270
1777-1987 1777 1987 0 0 0 0 0 8 0 0 0 1680
1843-1980 1843 1980 0 0 0 0 0 2 0 0 0 2080
1843-1981 1843 1981 0 0 0 0 0 3 0 0 0 2080
1843-1982 1843 1982 0 0 0 0 0 4 0 0 0 2080
1843-1983 1843 1983 0 0 0 0 0 5 0 0 0 2080
1843-1984 1843 1984 0 0 0 0 0 6 0 0 0 2080
1843-1985 1843 1985 0 0 0 0 0 7 0 0 0 2178
1843-1986 1843 1986 0 0 0 0 0 8 0 0 0 2184
1843-1987 1843 1987 0 0 0 0 0 9 0 0 0 2118
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1891-1981 1891 1981 0 0 0 0 0 3 0 0 0 1704
1891-1982 1891 1982 0 0 0 0 0 4 0 0 0 1472
1891-1983 1891 1983 0 0 0 0 0 5 0 0 0 2020
1891-1984 1891 1984 0 0 0 0 0 6 0 0 0 2000
1891-1985 1891 1985 0 0 0 0 0 7 0 0 0 2080
1891-1986 1891 1986 0 0 0 0 0 8 0 0 0 2080
1891-1987 1891 1987 0 0 0 0 0 9 0 0 0 2080
1895-1980 1895 1980 0 0 0 0 0 2 0 0 0 2115
1895-1981 1895 1981 0 0 0 0 0 3 0 0 0 2285
1895-1982 1895 1982 0 0 0 0 0 4 0 0 0 2080
1895-1983 1895 1983 0 0 0 0 0 5 0 0 0 2080
1895-1984 1895 1984 0 0 1 0 0 6 0 0 0 2080
1895-1985 1895 1985 0 0 0 0 0 7 0 0 0 2416
1895-1986 1895 1986 0 0 0 0 0 8 0 0 0 2184
1895-1987 1895 1987 0 0 0 0 0 9 0 0 0 2080
1899-1980 1899 1980 0 0 0 0 0 3 0 0 0 2080
1899-1981 1899 1981 0 0 0 0 0 4 0 0 0 2080
1899-1982 1899 1982 0 0 0 0 0 5 0 0 0 2080
1899-1983 1899 1983 0 0 0 0 0 6 0 0 0 2080
1899-1984 1899 1984 0 0 0 0 0 7 0 0 0 2080
1899-1985 1899 1985 0 0 0 0 0 8 0 0 0 2080
1899-1986 1899 1986 0 0 0 0 0 9 0 0 0 2080
1899-1987 1899 1987 0 0 0 0 0 10 0 0 0 2120
1925-1980 1925 1980 0 0 0 0 0 2 0 0 0 2752
1925-1981 1925 1981 0 0 0 0 0 3 0 0 0 2008
1925-1982 1925 1982 0 0 0 0 0 4 0 0 0 2501
1925-1983 1925 1983 0 0 0 0 0 5 0 0 0 2265
1925-1984 1925 1984 0 0 0 0 0 6 0 0 0 2188
1925-1985 1925 1985 0 0 0 0 0 7 0 0 0 2484
1925-1986 1925 1986 0 0 0 0 0 8 0 0 0 2228
1925-1987 1925 1987 0 0 0 0 0 9 0 0 0 2904
1930-1980 1930 1980 0 0 0 0 0 2 0 0 0 907
1930-1981 1930 1981 0 0 1 0 0 3 0 0 0 1217
1930-1982 1930 1982 0 0 0 0 0 4 0 0 0 800
1930-1983 1930 1983 0 0 0 0 0 5 0 0 0 1250
1930-1984 1930 1984 0 0 0 0 0 6 0 0 0 2080
1930-1985 1930 1985 0 0 0 0 0 7 1 0 0 2080
1930-1986 1930 1986 0 0 0 0 0 8 1 0 0 2080
1930-1987 1930 1987 0 0 0 0 0 9 1 0 0 2080
1961-1980 1961 1980 0 0 0 0 0 4 0 0 0 2912
1961-1981 1961 1981 0 0 1 0 0 5 0 0 0 2610
1961-1982 1961 1982 0 0 0 0 0 6 0 0 0 2600
1961-1983 1961 1983 0 0 1 0 0 7 0 0 0 2682
1961-1984 1961 1984 0 0 1 0 0 8 0 0 0 2745
1961-1985 1961 1985 0 0 1 0 0 9 0 0 0 2630
1961-1986 1961 1986 0 0 1 0 0 10 0 0 0 2220
1961-1987 1961 1987 0 0 1 0 0 11 0 0 0 2430
1963-1980 1963 1980 0 0 0 0 0 2 0 0 0 3328
1963-1981 1963 1981 0 0 0 0 0 3 0 0 0 3016
1963-1982 1963 1982 0 0 0 0 0 4 0 0 0 1928
1963-1983 1963 1983 0 0 0 0 0 5 0 0 0 2129
1963-1984 1963 1984 0 0 0 0 0 6 0 0 0 2444
1963-1985 1963 1985 0 0 0 0 0 7 0 0 0 2639
1963-1986 1963 1986 0 0 0 0 0 8 0 0 0 2858
1963-1987 1963 1987 0 0 0 0 0 9 0 0 0 3330
1979-1980 1979 1980 0 0 0 0 0 4 0 0 0 2040
1979-1981 1979 1981 0 0 0 0 0 5 0 0 0 1880
1979-1982 1979 1982 0 0 0 0 0 6 0 0 0 760
1979-1983 1979 1983 0 0 0 0 0 7 0 0 0 1840
1979-1984 1979 1984 0 0 0 0 0 8 0 0 0 2325
1979-1985 1979 1985 0 0 0 0 0 9 0 0 0 1945
1979-1986 1979 1986 0 0 0 0 0 10 0 0 0 2000
1979-1987 1979 1987 0 0 0 0 0 11 0 0 0 2080
1988-1980 1988 1980 0 0 0 1 0 2 0 0 0 2040
1988-1981 1988 1981 0 0 0 0 0 3 0 0 0 2120
1988-1982 1988 1982 0 0 0 0 0 4 0 0 0 2060
1988-1983 1988 1983 0 0 0 0 0 5 0 0 0 2080
1988-1984 1988 1984 0 0 0 0 0 6 0 0 0 2180
1988-1985 1988 1985 0 0 0 1 0 7 0 0 0 2130
1988-1986 1988 1986 0 0 0 0 0 8 0 0 0 2080
1988-1987 1988 1987 0 0 1 0 0 9 0 0 0 2480
2000-1980 2000 1980 0 0 0 0 0 3 0 0 0 2160
2000-1981 2000 1981 0 0 0 0 0 4 0 0 0 2260
2000-1982 2000 1982 0 0 0 0 0 5 0 0 0 1987
2000-1983 2000 1983 0 0 1 0 0 6 0 0 0 1620
2000-1984 2000 1984 0 0 0 0 0 7 0 0 0 3316
2000-1985 2000 1985 0 0 0 0 0 8 0 0 0 3154
2000-1986 2000 1986 0 0 0 0 0 9 0 0 0 3229
2000-1987 2000 1987 0 0 0 0 0 10 0 0 0 3288
2014-1980 2014 1980 0 0 0 0 0 2 0 0 0 920
2014-1981 2014 1981 0 0 0 0 0 3 0 0 0 1520
2014-1982 2014 1982 0 0 0 0 1 4 0 0 0 1476
2014-1983 2014 1983 0 0 0 0 1 5 0 0 0 2625
2014-1984 2014 1984 0 0 0 0 0 6 0 0 0 2255
2014-1985 2014 1985 0 0 0 0 0 7 0 0 0 2871
2014-1986 2014 1986 0 0 0 0 0 8 0 0 0 2072
2014-1987 2014 1987 0 0 0 0 0 9 0 0 0 1960
2025-1980 2025 1980 0 0 0 0 0 2 0 0 0 3010
2025-1981 2025 1981 0 0 0 0 0 3 0 0 0 3610
2025-1982 2025 1982 0 0 0 0 0 4 0 0 0 3393
2025-1983 2025 1983 0 0 0 0 0 5 0 0 0 3336
2025-1984 2025 1984 0 0 0 0 0 6 0 0 0 2502
2025-1985 2025 1985 0 0 0 0 0 7 0 0 0 2880
2025-1986 2025 1986 0 0 0 0 0 8 0 0 0 2949
2025-1987 2025 1987 0 0 0 0 0 9 0 0 0 4268
2038-1980 2038 1980 0 0 0 0 1 2 0 0 0 398
2038-1981 2038 1981 0 0 0 0 1 3 0 0 0 620
2038-1982 2038 1982 0 0 0 0 0 4 1 0 0 784
2038-1983 2038 1983 0 0 0 0 0 5 1 0 0 787
2038-1984 2038 1984 0 0 0 0 0 6 0 0 0 1067
2038-1985 2038 1985 0 0 0 0 0 7 0 0 0 1680
2038-1986 2038 1986 0 0 0 0 0 8 0 0 0 1790
2038-1987 2038 1987 0 0 1 0 0 9 0 0 0 2080
2075-1980 2075 1980 0 0 0 0 0 5 0 0 0 2140
2075-1981 2075 1981 0 0 0 0 0 6 0 0 0 1514
2075-1982 2075 1982 0 0 0 0 0 7 0 0 0 2264
2075-1983 2075 1983 0 0 0 0 0 8 0 0 0 1898
2075-1984 2075 1984 0 0 0 0 0 9 0 0 0 2480
2075-1985 2075 1985 0 0 0 0 0 10 0 0 0 2340
2075-1986 2075 1986 0 0 0 0 0 11 0 0 0 2340
2075-1987 2075 1987 0 0 0 0 0 12 0 0 0 2340
2101-1980 2101 1980 0 0 1 0 0 3 0 0 0 2080
2101-1981 2101 1981 0 0 0 0 0 4 0 0 0 2080
2101-1982 2101 1982 0 0 0 0 0 5 0 0 0 2080
2101-1983 2101 1983 0 0 0 0 0 6 0 0 0 2080
2101-1984 2101 1984 0 0 0 0 0 7 0 0 0 2080
2101-1985 2101 1985 0 0 0 0 0 8 0 0 0 2290
2101-1986 2101 1986 0 0 0 0 0 9 0 0 0 2535
2101-1987 2101 1987 0 0 0 0 0 10 0 0 0 2270
2106-1980 2106 1980 0 0 0 0 0 4 0 0 0 1655
2106-1981 2106 1981 0 0 0 0 0 5 0 0 0 2004
2106-1982 2106 1982 0 0 0 0 0 6 0 0 0 2060
2106-1983 2106 1983 0 0 0 0 0 7 0 0 0 2080
2106-1984 2106 1984 0 0 0 0 0 8 0 0 0 2080
2106-1985 2106 1985 0 0 0 0 0 9 0 0 0 2080
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2866-1985 2866 1985 0 0 0 0 0 8 0 0 0 3180
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2874-1985 2874 1985 0 0 0 0 0 9 0 1 0 2236
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2874-1987 2874 1987 0 0 0 0 0 11 0 1 0 1744
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2980-1985 2980 1985 0 0 0 0 0 7 0 0 0 1800
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2994-1983 2994 1983 0 0 0 0 0 6 0 0 0 3000
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2994-1985 2994 1985 0 0 0 0 0 8 0 0 0 3485
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3059-1983 3059 1983 1 0 0 0 0 8 0 0 0 2456
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3059-1985 3059 1985 1 0 0 0 0 10 0 0 0 2449
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3059-1987 3059 1987 1 0 0 0 0 12 0 0 0 2860
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3140-1985 3140 1985 0 0 0 0 0 8 0 0 0 2304
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3210-1983 3210 1983 0 0 0 0 0 5 0 0 0 1694
3210-1984 3210 1984 0 0 0 0 0 6 0 0 0 886
3210-1985 3210 1985 0 0 0 0 0 7 0 0 0 1179
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3215-1983 3215 1983 0 0 0 0 0 7 0 0 0 2080
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3219-1987 3219 1987 0 0 1 0 0 9 0 0 0 2820
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3226-1982 3226 1982 0 0 0 0 0 5 0 0 0 460
3226-1983 3226 1983 0 0 0 0 0 6 0 0 0 1136
3226-1984 3226 1984 0 0 0 0 0 7 0 0 0 1921
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3226-1987 3226 1987 0 0 0 0 0 10 0 0 0 2068
3235-1980 3235 1980 0 0 0 0 0 2 0 0 0 2000
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3235-1982 3235 1982 0 0 0 0 0 4 0 0 0 2728
3235-1983 3235 1983 0 0 0 0 0 5 0 0 0 3015
3235-1984 3235 1984 0 0 0 0 0 6 0 0 0 2700
3235-1985 3235 1985 0 0 0 0 0 7 0 0 0 2450
3235-1986 3235 1986 0 0 0 0 0 8 0 0 0 2130
3235-1987 3235 1987 0 0 0 0 0 9 0 0 0 1848
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3239-1983 3239 1983 0 1 0 0 0 4 0 0 0 532
3239-1984 3239 1984 0 1 0 0 0 5 0 0 0 676
3239-1985 3239 1985 0 1 0 0 0 6 0 0 0 2080
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3275-1985 3275 1985 0 0 1 0 0 6 0 0 0 2125
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3275-1987 3275 1987 0 0 1 0 0 8 0 0 0 675
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3289-1985 3289 1985 0 0 0 0 0 6 0 0 0 2056
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3333-1987 3333 1987 0 0 1 0 0 8 0 0 0 1296
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3353-1981 3353 1981 0 0 0 0 0 4 0 0 0 1900
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3353-1983 3353 1983 0 0 0 0 0 6 0 0 0 1772
3353-1984 3353 1984 0 0 0 0 0 7 0 0 0 2360
3353-1985 3353 1985 0 0 0 0 0 8 0 0 0 2016
3353-1986 3353 1986 0 0 1 0 0 9 0 0 0 1200
3353-1987 3353 1987 0 0 1 0 0 10 0 0 0 2204
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3380-1983 3380 1983 0 0 0 0 0 5 0 0 0 2372
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3401-1983 3401 1983 0 0 0 0 0 5 0 0 0 2688
3401-1984 3401 1984 0 0 0 0 0 6 0 0 0 2640
3401-1985 3401 1985 0 0 0 0 0 7 0 0 0 2274
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3414-1985 3414 1985 0 0 0 0 0 6 1 0 0 2444
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3461-1983 3461 1983 0 0 0 0 0 5 0 0 0 2786
3461-1984 3461 1984 0 0 1 0 0 6 0 0 0 2738
3461-1985 3461 1985 0 0 0 0 0 7 0 0 0 2544
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3461-1987 3461 1987 0 0 0 0 0 9 0 0 0 2235
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3468-1987 3468 1987 0 0 1 0 0 8 0 0 0 2682
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3495-1987 3495 1987 0 0 0 0 0 12 0 0 0 2305
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3563-1987 3563 1987 0 0 0 0 0 10 0 0 0 2216
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3581-1981 3581 1981 0 0 1 0 0 3 0 0 0 635
3581-1982 3581 1982 0 0 0 0 0 4 0 0 0 1800
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3581-1985 3581 1985 0 0 0 0 0 7 0 0 0 2288
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3589-1981 3589 1981 0 0 0 0 0 3 0 0 0 2112
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4607-1985 4607 1985 0 0 0 1 0 7 0 0 0 1880
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4607-1987 4607 1987 0 0 0 1 0 9 0 0 0 2360
4633-1980 4633 1980 0 0 0 0 0 3 0 0 0 2285
4633-1981 4633 1981 0 0 0 0 0 4 0 0 0 2120
4633-1982 4633 1982 0 0 0 0 0 5 0 0 0 2123
4633-1983 4633 1983 0 0 0 0 0 6 0 0 0 2175
4633-1984 4633 1984 0 0 0 0 0 7 0 0 0 2092
4633-1985 4633 1985 0 0 0 0 0 8 0 0 0 3270
4633-1986 4633 1986 0 0 0 0 0 9 0 0 0 3770
4633-1987 4633 1987 0 0 0 1 0 10 0 0 0 2710
4676-1980 4676 1980 0 0 0 0 0 2 0 0 0 2342
4676-1981 4676 1981 0 0 0 0 0 3 0 0 0 2196
4676-1982 4676 1982 0 0 0 0 0 4 0 0 0 1764
4676-1983 4676 1983 0 0 0 0 0 5 0 0 0 2080
4676-1984 4676 1984 0 0 0 0 0 6 0 0 0 2170
4676-1985 4676 1985 0 0 0 0 0 7 0 0 0 2184
4676-1986 4676 1986 0 0 0 0 0 8 0 0 0 2108
4676-1987 4676 1987 0 0 0 0 0 9 0 0 0 2144
4701-1980 4701 1980 0 0 0 0 0 2 1 0 0 1615
4701-1981 4701 1981 0 0 1 0 0 3 0 0 0 2064
4701-1982 4701 1982 0 0 1 0 0 4 0 0 0 2080
4701-1983 4701 1983 0 0 1 0 0 5 0 0 0 2285
4701-1984 4701 1984 0 0 0 0 0 6 0 0 0 2340
4701-1985 4701 1985 0 0 0 0 0 7 0 0 0 2130
4701-1986 4701 1986 0 0 0 0 0 8 1 0 0 2080
4701-1987 4701 1987 0 0 0 0 0 9 0 0 0 2080
4716-1980 4716 1980 1 0 0 0 0 3 0 0 0 3451
4716-1981 4716 1981 0 0 0 1 0 4 0 0 0 2100
4716-1982 4716 1982 0 0 0 0 0 5 0 0 0 2080
4716-1983 4716 1983 0 0 0 0 0 6 0 0 0 2892
4716-1984 4716 1984 0 0 0 0 0 7 0 0 0 2080
4716-1985 4716 1985 0 0 0 1 0 8 0 0 0 2080
4716-1986 4716 1986 0 0 0 0 0 9 0 0 0 2080
4716-1987 4716 1987 0 0 0 0 0 10 0 0 0 2080
4720-1980 4720 1980 0 0 0 0 0 5 0 0 0 2080
4720-1981 4720 1981 0 0 0 0 0 6 0 0 0 2080
4720-1982 4720 1982 0 0 0 0 0 7 0 0 0 2080
4720-1983 4720 1983 0 0 0 0 0 8 0 0 0 2080
4720-1984 4720 1984 0 0 0 0 0 9 0 0 0 2000
4720-1985 4720 1985 0 0 0 0 0 10 0 0 0 2080
4720-1986 4720 1986 0 0 0 0 0 11 0 0 0 2080
4720-1987 4720 1987 0 0 0 0 0 12 0 0 0 2080
4759-1980 4759 1980 0 0 0 0 0 4 0 0 0 1920
4759-1981 4759 1981 0 0 0 0 0 5 0 0 0 1600
4759-1982 4759 1982 0 0 0 0 0 6 0 0 0 2190
4759-1983 4759 1983 0 0 0 0 0 7 0 0 0 2782
4759-1984 4759 1984 0 0 0 0 0 8 0 0 0 2252
4759-1985 4759 1985 0 0 0 0 0 9 0 0 1 2080
4759-1986 4759 1986 0 0 0 0 0 10 0 0 0 2080
4759-1987 4759 1987 0 0 0 1 0 11 0 0 0 2080
4791-1980 4791 1980 0 0 0 0 0 5 0 0 0 2240
4791-1981 4791 1981 0 0 0 0 0 6 0 0 0 2600
4791-1982 4791 1982 0 0 0 0 0 7 0 0 0 2280
4791-1983 4791 1983 0 0 0 0 0 8 0 0 0 2400
4791-1984 4791 1984 0 0 0 0 0 9 0 0 0 2460
4791-1985 4791 1985 0 0 0 0 0 10 0 0 0 2460
4791-1986 4791 1986 0 0 0 0 0 11 0 0 0 2460
4791-1987 4791 1987 0 0 0 0 0 12 0 0 0 3262
4811-1980 4811 1980 0 0 0 0 0 2 0 0 0 1532
4811-1981 4811 1981 0 0 0 0 0 3 0 0 0 1748
4811-1982 4811 1982 0 0 0 0 0 4 0 0 1 1856
4811-1983 4811 1983 0 0 0 0 0 5 0 0 0 2276
4811-1984 4811 1984 0 0 0 0 0 6 0 0 0 2740
4811-1985 4811 1985 0 0 0 0 0 7 0 0 0 2634
4811-1986 4811 1986 0 0 0 0 0 8 0 0 0 2600
4811-1987 4811 1987 0 0 0 0 0 9 0 0 0 2600
4828-1980 4828 1980 0 0 0 0 0 2 0 0 0 1416
4828-1981 4828 1981 0 0 0 0 0 3 0 0 0 2175
4828-1982 4828 1982 0 0 1 0 0 4 0 0 0 3040
4828-1983 4828 1983 0 0 1 0 0 5 0 0 0 2436
4828-1984 4828 1984 0 0 1 0 0 6 0 0 0 3250
4828-1985 4828 1985 0 0 0 0 0 7 0 0 0 1420
4828-1986 4828 1986 0 0 0 0 0 8 0 0 0 1794
4828-1987 4828 1987 0 0 0 0 0 9 0 0 0 1665
manuf married min nrthcen nrtheast occ1 occ2 occ3 occ4 occ5 occ6 occ7
13-1980 0 0 0 0 1 0 0 0 0 0 0 0
13-1981 0 0 0 0 1 0 0 0 0 0 0 0
13-1982 0 0 0 0 1 0 0 0 0 0 0 0
13-1983 0 0 0 0 1 0 0 0 0 0 0 0
13-1984 0 0 0 0 1 0 0 0 0 1 0 0
13-1985 0 0 0 0 1 0 1 0 0 0 0 0
13-1986 0 0 0 0 1 0 1 0 0 0 0 0
13-1987 0 0 0 0 1 0 1 0 0 0 0 0
17-1980 0 0 0 0 1 0 1 0 0 0 0 0
17-1981 0 0 0 0 1 0 1 0 0 0 0 0
17-1982 0 0 0 0 1 0 1 0 0 0 0 0
17-1983 0 0 0 0 1 0 1 0 0 0 0 0
17-1984 0 0 0 0 1 0 1 0 0 0 0 0
17-1985 0 0 0 0 1 0 0 0 0 0 0 1
17-1986 0 0 0 0 1 0 0 0 0 0 0 1
17-1987 0 0 0 0 1 0 0 0 0 1 0 0
18-1980 0 1 0 0 0 0 0 0 1 0 0 0
18-1981 0 1 0 0 0 0 0 0 1 0 0 0
18-1982 1 1 0 0 0 0 1 0 0 0 0 0
18-1983 0 1 0 0 0 0 0 1 0 0 0 0
18-1984 0 1 0 0 0 0 0 1 0 0 0 0
18-1985 0 1 0 0 0 0 0 1 0 0 0 0
18-1986 0 1 0 0 0 0 0 1 0 0 0 0
18-1987 0 1 0 0 0 0 0 1 0 0 0 0
45-1980 0 0 0 0 1 0 0 0 0 0 0 1
45-1981 0 0 0 0 1 0 0 0 0 0 1 0
45-1982 1 0 0 0 1 0 0 0 0 0 1 0
45-1983 1 0 0 0 1 0 0 0 0 0 1 0
45-1984 0 0 0 0 1 0 0 0 0 0 1 0
45-1985 1 0 0 0 1 0 0 0 0 0 1 0
45-1986 0 0 0 0 1 0 0 0 1 0 0 0
45-1987 0 1 0 0 1 0 0 0 1 0 0 0
110-1980 0 0 0 0 1 0 0 0 1 0 0 0
110-1981 0 0 0 0 1 0 0 0 1 0 0 0
110-1982 0 0 0 0 1 0 1 0 0 0 0 0
110-1983 0 0 0 0 1 0 1 0 0 0 0 0
110-1984 0 1 0 0 1 1 0 0 0 0 0 0
110-1985 0 1 0 0 1 1 0 0 0 0 0 0
110-1986 0 1 0 0 1 0 0 0 1 0 0 0
110-1987 0 1 0 0 1 0 0 0 1 0 0 0
120-1980 0 0 0 0 1 0 0 0 0 0 0 0
120-1981 0 0 0 0 1 0 0 0 0 0 0 0
120-1982 0 0 0 0 1 0 0 0 0 0 0 0
120-1983 0 0 0 0 1 0 0 0 0 0 0 0
120-1984 0 0 0 0 1 0 0 0 0 0 0 0
120-1985 0 0 0 0 1 0 0 0 0 0 0 0
120-1986 0 0 0 0 1 0 0 0 1 0 0 0
120-1987 0 0 0 0 1 0 0 0 1 0 0 0
126-1980 0 0 0 0 1 0 0 1 0 0 0 0
126-1981 0 0 0 0 1 0 1 0 0 0 0 0
126-1982 0 0 0 0 1 0 1 0 0 0 0 0
126-1983 0 0 0 0 1 0 0 1 0 0 0 0
126-1984 0 0 0 0 1 0 0 1 0 0 0 0
126-1985 0 1 0 0 1 0 0 1 0 0 0 0
126-1986 0 1 0 0 1 0 0 1 0 0 0 0
126-1987 0 1 0 0 1 0 1 0 0 0 0 0
150-1980 0 0 0 0 1 0 0 0 0 0 1 0
150-1981 0 0 0 0 1 0 0 0 0 0 1 0
150-1982 0 0 0 0 1 0 0 0 0 0 1 0
150-1983 0 0 0 0 1 0 0 0 0 0 1 0
150-1984 0 0 0 0 1 0 0 0 0 0 0 0
150-1985 0 0 0 0 1 0 0 0 0 0 0 0
150-1986 0 0 0 0 1 0 0 0 0 0 1 0
150-1987 0 0 0 0 1 0 0 0 0 0 0 0
162-1980 0 0 0 0 1 0 0 0 1 0 0 0
162-1981 0 0 0 0 1 0 0 0 1 0 0 0
162-1982 1 0 0 0 1 0 0 1 0 0 0 0
162-1983 0 0 0 0 1 0 0 0 0 0 0 1
162-1984 0 0 0 0 1 0 1 0 0 0 0 0
162-1985 0 0 0 0 1 0 1 0 0 0 0 0
162-1986 0 0 0 0 1 0 1 0 0 0 0 0
162-1987 0 0 0 0 0 0 1 0 0 0 0 0
166-1980 0 0 0 0 1 0 0 0 0 0 0 1
166-1981 0 0 0 0 1 0 0 0 0 0 0 1
166-1982 0 0 0 0 1 0 0 0 0 0 0 1
166-1983 0 0 0 0 1 0 0 0 1 0 0 0
166-1984 0 0 0 0 1 0 0 0 1 0 0 0
166-1985 0 0 0 0 1 0 0 0 0 1 0 0
166-1986 0 1 0 0 1 0 1 0 0 0 0 0
166-1987 0 1 0 0 1 0 0 0 0 1 0 0
189-1980 0 0 0 0 1 0 0 0 1 0 0 0
189-1981 0 0 0 0 1 0 0 0 1 0 0 0
189-1982 0 0 0 0 1 0 0 0 1 0 0 0
189-1983 0 0 0 0 1 0 0 1 0 0 0 0
189-1984 0 0 0 0 1 0 0 0 1 0 0 0
189-1985 0 0 0 0 1 0 0 1 0 0 0 0
189-1986 1 0 0 0 1 0 0 0 1 0 0 0
189-1987 1 0 0 0 1 0 0 0 1 0 0 0
193-1980 1 0 0 0 1 1 0 0 0 0 0 0
193-1981 1 0 0 0 1 1 0 0 0 0 0 0
193-1982 1 0 0 0 1 1 0 0 0 0 0 0
193-1983 1 0 0 0 1 1 0 0 0 0 0 0
193-1984 1 0 0 0 1 1 0 0 0 0 0 0
193-1985 1 1 0 0 1 1 0 0 0 0 0 0
193-1986 1 1 0 0 1 1 0 0 0 0 0 0
193-1987 1 1 0 0 1 1 0 0 0 0 0 0
209-1980 0 0 0 0 1 0 0 0 0 0 0 0
209-1981 0 0 0 0 1 0 0 0 0 0 0 0
209-1982 0 0 0 0 1 0 0 0 0 0 0 0
209-1983 0 0 0 0 1 0 0 0 0 0 0 0
209-1984 0 0 0 0 1 0 0 0 0 0 0 0
209-1985 0 0 0 0 1 0 1 0 0 0 0 0
209-1986 0 0 0 0 1 0 1 0 0 0 0 0
209-1987 0 0 0 0 1 0 1 0 0 0 0 0
212-1980 1 0 0 0 1 0 0 0 0 1 0 0
212-1981 1 0 0 0 1 0 0 0 0 0 1 0
212-1982 1 0 0 0 1 0 0 0 0 0 1 0
212-1983 1 0 0 0 1 0 0 0 0 0 1 0
212-1984 1 0 0 0 1 0 0 0 1 0 0 0
212-1985 1 0 0 0 1 0 0 0 0 0 1 0
212-1986 1 1 0 0 1 0 0 0 0 0 1 0
212-1987 1 1 0 0 1 0 0 0 0 0 1 0
218-1980 0 0 0 0 1 1 0 0 0 0 0 0
218-1981 0 0 0 0 1 1 0 0 0 0 0 0
218-1982 0 0 0 0 1 0 0 0 1 0 0 0
218-1983 0 1 0 0 1 1 0 0 0 0 0 0
218-1984 0 1 0 0 1 1 0 0 0 0 0 0
218-1985 0 1 0 0 1 0 0 0 1 0 0 0
218-1986 0 1 0 0 1 0 1 0 0 0 0 0
218-1987 0 1 0 0 1 0 1 0 0 0 0 0
243-1980 0 0 0 0 1 0 0 0 0 1 0 0
243-1981 0 0 0 0 1 0 1 0 0 0 0 0
243-1982 0 0 0 0 1 0 1 0 0 0 0 0
243-1983 0 1 0 0 1 0 1 0 0 0 0 0
243-1984 0 1 0 0 1 0 1 0 0 0 0 0
243-1985 0 1 0 0 1 0 1 0 0 0 0 0
243-1986 0 1 0 0 1 0 1 0 0 0 0 0
243-1987 0 1 0 0 1 0 1 0 0 0 0 0
259-1980 1 1 0 0 1 0 0 0 0 1 0 0
259-1981 1 1 0 0 1 0 0 0 0 1 0 0
259-1982 1 1 0 0 1 0 0 0 0 1 0 0
259-1983 1 1 0 0 1 0 0 0 0 1 0 0
259-1984 1 1 0 0 1 0 0 0 0 0 1 0
259-1985 0 1 0 0 1 0 0 0 0 0 1 0
259-1986 0 1 0 0 1 0 0 0 0 1 0 0
259-1987 0 1 0 0 1 0 0 0 0 0 1 0
260-1980 0 0 0 0 1 0 0 0 1 0 0 0
260-1981 0 0 0 0 1 0 0 0 0 0 0 1
260-1982 1 0 0 0 1 0 0 0 0 0 1 0
260-1983 1 1 0 0 1 1 0 0 0 0 0 0
260-1984 1 1 0 0 1 1 0 0 0 0 0 0
260-1985 1 1 0 0 1 1 0 0 0 0 0 0
260-1986 1 1 0 0 1 0 0 0 0 0 1 0
260-1987 1 1 0 0 1 0 0 0 0 1 0 0
309-1980 0 0 0 1 0 0 0 0 0 0 1 0
309-1981 0 0 0 0 1 0 0 0 0 0 1 0
309-1982 0 0 0 0 1 0 0 0 0 0 1 0
309-1983 0 1 0 0 1 0 0 0 0 1 0 0
309-1984 0 1 0 0 1 0 0 0 0 0 1 0
309-1985 0 1 0 0 1 0 0 0 0 1 0 0
309-1986 0 1 0 0 1 0 0 0 0 0 1 0
309-1987 1 1 0 0 1 0 0 0 0 0 1 0
351-1980 0 0 0 0 1 0 0 0 1 0 0 0
351-1981 0 0 0 0 1 0 0 0 1 0 0 0
351-1982 0 1 0 0 1 0 0 0 1 0 0 0
351-1983 0 1 0 0 1 0 0 0 1 0 0 0
351-1984 0 1 0 0 1 0 0 0 1 0 0 0
351-1985 0 1 0 0 1 0 0 0 1 0 0 0
351-1986 0 1 0 0 1 1 0 0 0 0 0 0
351-1987 0 1 0 0 1 1 0 0 0 0 0 0
353-1980 1 0 0 0 1 0 0 0 0 0 1 0
353-1981 1 0 0 0 1 0 0 0 0 0 1 0
353-1982 0 0 0 0 1 0 0 0 0 1 0 0
353-1983 1 0 0 0 1 0 0 0 0 0 1 0
353-1984 1 0 0 0 1 0 0 0 0 1 0 0
353-1985 0 0 0 0 1 0 0 0 0 1 0 0
353-1986 1 0 0 0 1 0 0 0 0 1 0 0
353-1987 0 0 0 0 1 0 0 0 0 1 0 0
383-1980 1 0 0 0 1 0 0 0 0 0 1 0
383-1981 1 0 0 0 1 0 0 0 0 0 1 0
383-1982 1 0 0 0 1 0 0 0 0 0 1 0
383-1983 1 0 0 0 1 0 0 0 1 0 0 0
383-1984 1 0 0 0 1 0 0 0 1 0 0 0
383-1985 1 0 0 0 1 0 0 0 0 1 0 0
383-1986 1 0 0 0 1 0 0 0 0 1 0 0
383-1987 1 0 0 0 1 0 0 0 0 1 0 0
408-1980 1 0 0 0 1 0 0 0 0 1 0 0
408-1981 1 1 0 0 1 0 0 0 0 0 1 0
408-1982 1 1 0 0 1 0 0 0 0 1 0 0
408-1983 1 1 0 0 1 0 0 0 0 1 0 0
408-1984 1 1 0 0 1 0 0 0 0 1 0 0
408-1985 1 1 0 0 1 0 0 0 0 1 0 0
408-1986 1 1 0 0 1 0 0 0 0 1 0 0
408-1987 1 1 0 0 1 0 0 0 0 1 0 0
424-1980 1 1 0 0 1 0 0 0 0 1 0 0
424-1981 1 1 0 0 1 0 0 0 0 1 0 0
424-1982 1 1 0 0 1 0 0 0 0 1 0 0
424-1983 1 1 0 0 1 0 0 0 0 0 1 0
424-1984 1 1 0 0 1 0 0 0 0 1 0 0
424-1985 1 1 0 0 1 0 0 0 0 1 0 0
424-1986 1 1 0 0 1 0 0 0 0 1 0 0
424-1987 1 1 0 0 1 0 0 0 0 1 0 0
464-1980 0 0 0 0 1 0 1 0 0 0 0 0
464-1981 0 0 0 0 1 0 0 1 0 0 0 0
464-1982 0 1 0 0 1 0 1 0 0 0 0 0
464-1983 0 1 0 0 1 0 0 0 1 0 0 0
464-1984 0 1 0 0 1 0 0 0 0 0 1 0
464-1985 0 1 0 0 1 0 0 1 0 0 0 0
464-1986 0 1 0 0 1 0 0 1 0 0 0 0
464-1987 0 1 0 0 1 0 0 1 0 0 0 0
483-1980 1 0 0 1 0 0 0 0 0 1 0 0
483-1981 1 0 0 1 0 0 1 0 0 0 0 0
483-1982 1 0 0 1 0 0 0 0 0 1 0 0
483-1983 1 0 0 1 0 0 0 0 0 0 0 1
483-1984 1 0 0 1 0 0 0 0 0 0 1 0
483-1985 1 0 0 1 0 0 0 0 1 0 0 0
483-1986 1 0 0 1 0 0 0 0 0 0 1 0
483-1987 1 0 0 1 0 0 0 0 0 0 1 0
556-1980 0 0 0 1 0 0 0 0 0 0 0 0
556-1981 0 0 0 1 0 1 0 0 0 0 0 0
556-1982 0 0 0 1 0 1 0 0 0 0 0 0
556-1983 0 0 0 1 0 0 1 0 0 0 0 0
556-1984 0 0 0 1 0 1 0 0 0 0 0 0
556-1985 0 0 0 1 0 0 1 0 0 0 0 0
556-1986 0 0 0 1 0 1 0 0 0 0 0 0
556-1987 0 0 0 1 0 0 1 0 0 0 0 0
560-1980 0 0 0 0 0 0 0 0 0 0 0 0
560-1981 0 0 0 0 0 0 0 0 0 0 0 0
560-1982 0 0 0 0 0 0 0 0 0 0 0 0
560-1983 0 0 0 0 0 0 0 1 0 0 0 0
560-1984 0 0 0 0 0 1 0 0 0 0 0 0
560-1985 0 0 0 0 0 0 1 0 0 0 0 0
560-1986 0 0 0 0 0 0 1 0 0 0 0 0
560-1987 0 0 0 0 0 1 0 0 0 0 0 0
569-1980 0 0 0 1 0 0 1 0 0 0 0 0
569-1981 0 0 0 1 0 0 0 1 0 0 0 0
569-1982 0 0 0 1 0 0 1 0 0 0 0 0
569-1983 0 0 0 1 0 0 0 1 0 0 0 0
569-1984 1 0 0 1 0 0 1 0 0 0 0 0
569-1985 0 0 0 1 0 0 0 1 0 0 0 0
569-1986 0 0 0 1 0 0 0 1 0 0 0 0
569-1987 0 0 0 1 0 1 0 0 0 0 0 0
583-1980 0 0 0 1 0 0 1 0 0 0 0 0
583-1981 1 0 0 1 0 0 0 0 0 1 0 0
583-1982 1 0 0 1 0 0 0 0 0 1 0 0
583-1983 1 0 0 1 0 0 0 0 0 0 1 0
583-1984 1 1 0 1 0 0 0 0 0 1 0 0
583-1985 1 1 0 1 0 0 0 0 0 1 0 0
583-1986 1 1 0 1 0 0 0 0 0 1 0 0
583-1987 1 0 0 1 0 0 0 0 0 1 0 0
647-1980 1 0 0 1 0 0 0 0 0 0 1 0
647-1981 1 1 0 1 0 0 0 0 1 0 0 0
647-1982 1 1 0 1 0 0 0 0 1 0 0 0
647-1983 1 1 0 1 0 0 0 0 1 0 0 0
647-1984 1 0 0 1 0 0 0 0 1 0 0 0
647-1985 1 1 0 1 0 0 0 0 1 0 0 0
647-1986 0 1 0 1 0 0 0 0 1 0 0 0
647-1987 0 1 0 1 0 0 0 0 1 0 0 0
658-1980 1 0 0 1 0 0 0 0 1 0 0 0
658-1981 1 0 0 1 0 0 0 0 1 0 0 0
658-1982 1 0 0 1 0 0 0 0 0 0 1 0
658-1983 1 0 0 1 0 0 0 0 1 0 0 0
658-1984 1 0 0 1 0 0 0 0 1 0 0 0
658-1985 1 0 0 1 0 0 0 0 0 0 1 0
658-1986 1 0 0 1 0 0 0 0 1 0 0 0
658-1987 0 0 0 1 0 0 0 0 1 0 0 0
684-1980 1 0 0 1 0 0 0 0 0 0 1 0
684-1981 1 0 0 1 0 0 0 0 0 0 1 0
684-1982 1 1 0 1 0 0 0 0 0 1 0 0
684-1983 1 1 0 1 0 0 0 0 0 0 1 0
684-1984 1 1 0 1 0 0 0 0 0 0 1 0
684-1985 1 1 0 1 0 0 0 0 0 0 0 1
684-1986 1 1 0 1 0 0 0 0 0 0 0 1
684-1987 0 1 0 1 0 1 0 0 0 0 0 0
711-1980 0 0 0 1 0 0 0 0 0 0 0 1
711-1981 0 0 0 1 0 0 0 0 0 0 0 1
711-1982 0 0 0 1 0 0 1 0 0 0 0 0
711-1983 0 0 0 1 0 0 0 0 0 1 0 0
711-1984 0 0 0 1 0 0 0 0 0 0 0 1
711-1985 0 0 0 1 0 0 0 1 0 0 0 0
711-1986 0 0 0 1 0 0 0 1 0 0 0 0
711-1987 0 0 0 1 0 0 0 1 0 0 0 0
729-1980 0 1 0 1 0 0 0 0 0 0 0 1
729-1981 0 0 0 1 0 0 0 0 0 0 0 1
729-1982 0 1 0 1 0 0 1 0 0 0 0 0
729-1983 0 1 0 1 0 0 0 0 0 0 0 1
729-1984 1 1 0 0 0 0 0 1 0 0 0 0
729-1985 1 1 0 0 0 0 0 1 0 0 0 0
729-1986 0 1 0 0 0 0 1 0 0 0 0 0
729-1987 1 1 0 0 0 0 0 1 0 0 0 0
731-1980 0 0 0 1 0 0 1 0 0 0 0 0
731-1981 0 1 0 1 0 0 0 0 0 0 0 0
731-1982 0 1 0 1 0 0 0 0 0 0 0 0
731-1983 0 1 0 1 0 0 0 0 0 0 0 0
731-1984 1 1 0 1 0 0 0 0 0 1 0 0
731-1985 0 0 0 1 0 0 0 0 0 0 0 1
731-1986 0 0 0 1 0 0 0 0 0 0 0 0
731-1987 1 0 0 1 0 0 0 0 0 0 1 0
732-1980 1 0 0 1 0 0 0 0 0 0 1 0
732-1981 1 0 0 1 0 0 0 0 0 0 1 0
732-1982 1 0 0 1 0 0 0 0 0 0 1 0
732-1983 1 0 0 1 0 0 0 0 0 0 1 0
732-1984 1 0 0 1 0 0 0 0 0 0 1 0
732-1985 1 0 0 1 0 0 0 0 0 0 1 0
732-1986 1 0 0 1 0 0 0 0 0 0 1 0
732-1987 1 0 0 1 0 0 0 0 0 0 1 0
793-1980 0 0 0 1 0 0 0 0 1 0 0 0
793-1981 0 0 0 1 0 0 0 0 0 0 0 0
793-1982 0 0 0 1 0 0 0 0 0 0 0 0
793-1983 0 0 0 1 0 0 0 0 0 0 0 0
793-1984 0 0 0 1 0 1 0 0 0 0 0 0
793-1985 0 0 0 1 0 0 1 0 0 0 0 0
793-1986 0 0 0 1 0 0 1 0 0 0 0 0
793-1987 0 0 0 1 0 0 0 0 0 0 0 0
797-1980 0 0 0 1 0 0 0 0 0 0 0 1
797-1981 1 0 0 1 0 0 0 0 0 1 0 0
797-1982 1 0 0 1 0 0 1 0 0 0 0 0
797-1983 0 1 0 1 0 0 0 0 0 0 0 1
797-1984 1 1 0 1 0 0 0 0 0 0 1 0
797-1985 1 1 0 1 0 0 0 0 0 0 1 0
797-1986 0 1 0 1 0 0 0 0 0 0 1 0
797-1987 0 1 0 1 0 0 0 0 0 0 1 0
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800-1981 0 0 0 1 0 0 0 0 0 0 0 0
800-1982 0 0 0 1 0 0 0 0 0 0 0 0
800-1983 0 0 0 1 0 0 0 0 0 0 0 0
800-1984 0 0 0 1 0 0 0 0 0 0 0 0
800-1985 0 0 0 1 0 0 0 0 0 0 0 0
800-1986 0 1 0 1 0 0 0 0 0 0 0 0
800-1987 0 1 0 1 0 0 0 0 0 1 0 0
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813-1981 0 0 0 1 0 1 0 0 0 0 0 0
813-1982 0 0 0 1 0 0 0 0 1 0 0 0
813-1983 0 0 0 1 0 1 0 0 0 0 0 0
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813-1985 0 0 0 1 0 1 0 0 0 0 0 0
813-1986 0 0 0 1 0 0 0 0 1 0 0 0
813-1987 0 0 0 1 0 1 0 0 0 0 0 0
823-1980 0 0 0 1 0 0 0 0 0 0 0 0
823-1981 0 0 0 1 0 0 0 0 1 0 0 0
823-1982 0 0 0 1 0 0 0 1 0 0 0 0
823-1983 0 0 0 1 0 0 0 0 0 0 0 0
823-1984 0 0 0 1 0 0 0 0 0 0 0 0
823-1985 0 0 0 1 0 0 0 1 0 0 0 0
823-1986 0 0 0 1 0 0 1 0 0 0 0 0
823-1987 0 0 0 0 0 0 0 1 0 0 0 0
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827-1981 0 0 0 1 0 0 0 0 0 1 0 0
827-1982 0 0 0 1 0 0 0 0 0 0 0 0
827-1983 0 0 0 1 0 0 0 0 0 0 0 0
827-1984 0 0 0 1 0 0 0 1 0 0 0 0
827-1985 1 0 0 1 0 0 0 1 0 0 0 0
827-1986 1 1 0 1 0 0 0 1 0 0 0 0
827-1987 0 1 0 1 0 0 0 1 0 0 0 0
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847-1981 0 0 0 1 0 1 0 0 0 0 0 0
847-1982 0 0 0 0 1 0 0 0 0 1 0 0
847-1983 0 0 0 0 1 0 0 0 0 1 0 0
847-1984 1 0 0 0 1 0 0 0 0 1 0 0
847-1985 0 0 0 0 1 0 0 0 1 0 0 0
847-1986 0 0 0 0 1 0 1 0 0 0 0 0
847-1987 0 1 0 0 1 0 0 0 1 0 0 0
851-1980 1 0 0 1 0 0 0 0 0 0 1 0
851-1981 1 0 0 1 0 0 0 0 0 0 1 0
851-1982 1 1 0 1 0 0 0 0 0 0 1 0
851-1983 1 1 0 1 0 0 0 0 0 1 0 0
851-1984 1 1 0 1 0 0 0 0 0 0 0 1
851-1985 1 1 0 1 0 0 0 0 0 1 0 0
851-1986 1 1 0 1 0 0 0 0 0 1 0 0
851-1987 1 0 0 1 0 0 0 0 0 1 0 0
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863-1985 0 1 0 1 0 0 0 0 1 0 0 0
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863-1987 0 1 0 1 0 1 0 0 0 0 0 0
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873-1981 0 0 0 1 0 0 0 0 0 0 0 0
873-1982 1 0 0 1 0 0 0 0 0 0 0 0
873-1983 1 0 0 1 0 0 0 0 0 0 0 0
873-1984 0 0 0 1 0 0 0 0 0 0 0 0
873-1985 0 0 0 1 0 1 0 0 0 0 0 0
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891-1981 0 1 0 1 0 0 0 0 0 0 1 0
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4633-1986 0 1 0 0 0 0 1 0 0 0 0 0
4633-1987 0 1 0 0 0 0 0 0 0 0 1 0
4676-1980 0 0 0 0 1 0 0 0 0 0 0 0
4676-1981 0 0 0 0 1 0 0 0 0 0 1 0
4676-1982 0 0 0 0 1 0 0 0 0 0 1 0
4676-1983 1 0 0 0 1 0 0 0 0 0 1 0
4676-1984 1 0 0 0 1 0 0 0 0 1 0 0
4676-1985 0 0 0 0 1 0 0 0 0 1 0 0
4676-1986 1 0 0 0 1 0 0 0 0 1 0 0
4676-1987 1 0 0 0 1 0 0 0 0 1 0 0
4701-1980 0 0 0 0 1 0 0 0 1 0 0 0
4701-1981 0 0 0 0 1 0 0 0 0 1 0 0
4701-1982 0 0 0 0 1 1 0 0 0 0 0 0
4701-1983 0 0 0 0 1 1 0 0 0 0 0 0
4701-1984 0 0 0 0 1 1 0 0 0 0 0 0
4701-1985 0 1 0 0 1 0 0 0 1 0 0 0
4701-1986 0 1 0 0 1 0 1 0 0 0 0 0
4701-1987 0 1 0 0 1 0 1 0 0 0 0 0
4716-1980 0 1 0 0 1 0 0 0 0 0 0 0
4716-1981 0 1 0 0 1 0 0 0 0 0 0 1
4716-1982 0 1 0 0 1 0 0 0 0 0 1 0
4716-1983 0 1 0 0 1 0 0 0 0 1 0 0
4716-1984 0 1 0 0 1 0 0 0 0 1 0 0
4716-1985 0 1 0 0 1 0 0 0 0 1 0 0
4716-1986 0 1 0 0 1 0 0 0 0 1 0 0
4716-1987 0 1 0 0 1 0 0 0 0 1 0 0
4720-1980 0 1 0 1 0 0 0 0 0 1 0 0
4720-1981 0 1 0 1 0 0 0 0 0 1 0 0
4720-1982 0 1 0 1 0 0 0 0 0 1 0 0
4720-1983 0 1 0 1 0 0 0 0 0 1 0 0
4720-1984 0 1 0 1 0 0 0 0 0 1 0 0
4720-1985 0 1 0 1 0 0 0 0 0 0 0 0
4720-1986 0 1 0 1 0 0 0 0 0 0 1 0
4720-1987 0 1 0 1 0 0 0 0 0 0 0 0
4759-1980 1 0 0 1 0 0 0 0 0 0 1 0
4759-1981 1 1 0 1 0 0 0 0 0 0 1 0
4759-1982 1 1 0 1 0 0 0 0 0 0 1 0
4759-1983 1 1 0 1 0 0 0 0 0 0 1 0
4759-1984 0 1 0 1 0 0 0 0 0 0 1 0
4759-1985 1 1 0 1 0 0 0 0 0 0 1 0
4759-1986 1 1 0 1 0 0 0 0 0 0 1 0
4759-1987 0 1 0 1 0 0 0 0 0 0 1 0
4791-1980 1 1 0 1 0 0 0 0 0 0 1 0
4791-1981 1 1 0 1 0 0 0 0 0 0 1 0
4791-1982 1 1 0 1 0 0 0 0 0 1 0 0
4791-1983 1 1 0 1 0 0 0 0 0 0 1 0
4791-1984 1 1 0 1 0 0 0 0 0 1 0 0
4791-1985 1 1 0 1 0 0 0 0 0 0 1 0
4791-1986 1 1 0 1 0 0 0 0 0 0 1 0
4791-1987 1 1 0 1 0 0 0 0 0 1 0 0
4811-1980 0 0 0 1 0 0 0 0 0 0 1 0
4811-1981 0 0 0 1 0 0 0 0 0 0 1 0
4811-1982 0 0 0 1 0 0 0 0 0 0 1 0
4811-1983 0 0 0 1 0 0 0 0 0 0 1 0
4811-1984 1 0 0 1 0 0 0 0 0 1 0 0
4811-1985 1 0 0 1 0 0 0 0 0 0 1 0
4811-1986 1 0 0 1 0 0 0 0 0 0 1 0
4811-1987 1 0 0 1 0 0 0 0 0 1 0 0
4828-1980 0 0 0 1 0 0 0 0 0 0 0 0
4828-1981 0 0 0 0 0 0 0 0 0 0 0 0
4828-1982 0 0 0 0 0 0 0 0 1 0 0 0
4828-1983 0 0 0 0 0 0 1 0 0 0 0 0
4828-1984 0 0 0 0 0 0 1 0 0 0 0 0
4828-1985 0 0 0 0 0 0 0 0 0 0 0 0
4828-1986 0 1 0 1 0 0 0 0 0 0 0 0
4828-1987 0 1 0 1 0 0 0 0 0 0 0 0
occ8 occ9 per pro pub rur south educ tra trad union lwage d81
13-1980 0 1 0 0 0 0 0 14 0 0 0 1.197540164 0
13-1981 0 1 1 0 0 0 0 14 0 0 1 1.853060007 1
13-1982 0 1 0 0 0 0 0 14 0 0 0 1.344461679 0
13-1983 0 1 0 0 0 0 0 14 0 0 0 1.433213353 0
13-1984 0 0 1 0 0 0 0 14 0 0 0 1.568125129 0
13-1985 0 0 0 0 0 0 0 14 0 0 0 1.699890971 0
13-1986 0 0 0 0 0 0 0 14 0 0 0 -0.720262587 0
13-1987 0 0 0 0 0 0 0 14 0 0 0 1.669187903 0
17-1980 0 0 0 0 0 0 0 13 0 1 0 1.675962448 0
17-1981 0 0 0 0 0 0 0 13 0 1 0 1.518398166 1
17-1982 0 0 0 0 0 0 0 13 0 1 0 1.559190512 0
17-1983 0 0 0 0 0 0 0 13 0 1 0 1.725410104 0
17-1984 0 0 0 0 0 0 0 13 0 1 0 1.622022271 0
17-1985 0 0 0 0 0 0 0 13 0 0 0 1.608588219 0
17-1986 0 0 0 0 0 0 0 13 0 0 0 1.572385430 0
17-1987 0 0 0 0 0 0 0 13 0 0 0 1.820333838 0
18-1980 0 0 0 0 0 0 0 12 0 1 0 1.515962720 0
18-1981 0 0 0 0 0 0 0 12 0 1 0 1.735379100 1
18-1982 0 0 0 0 0 0 0 12 0 0 0 1.631743670 0
18-1983 0 0 0 0 0 0 0 12 0 1 0 1.998228788 0
18-1984 0 0 0 0 0 0 0 12 0 1 0 2.184014320 0
18-1985 0 0 0 0 0 0 0 12 0 1 0 2.266662121 0
18-1986 0 0 0 0 0 0 0 12 0 1 0 2.069943905 0
18-1987 0 0 0 0 0 0 0 12 0 1 0 2.873160839 0
45-1980 0 0 0 0 0 0 0 12 1 0 1 1.894114971 0
45-1981 0 0 0 0 0 0 0 12 1 0 1 1.471159339 1
45-1982 0 0 0 0 0 0 0 12 0 0 0 1.473497510 0
45-1983 0 0 0 0 0 0 0 12 0 0 0 1.740914226 0
45-1984 0 0 0 0 0 0 0 12 0 0 0 1.823213696 0
45-1985 0 0 0 0 0 0 0 12 0 0 0 1.908272862 0
45-1986 0 0 0 0 0 0 0 12 1 0 0 1.742447376 0
45-1987 0 0 0 0 0 0 0 12 0 0 0 2.135689020 0
110-1980 0 0 0 1 0 0 0 12 0 0 1 1.948774815 0
110-1981 0 0 0 1 0 0 0 12 0 0 0 1.962259293 1
110-1982 0 0 0 1 0 0 0 12 0 0 0 1.963296771 0
110-1983 0 0 0 1 0 0 0 12 0 0 0 2.202515602 0
110-1984 0 0 0 0 0 0 0 12 0 1 0 2.134954214 0
110-1985 0 0 0 0 0 0 0 12 0 0 0 2.125822783 0
110-1986 0 0 0 0 0 0 0 12 0 0 0 1.991016626 0
110-1987 0 0 0 0 0 0 0 12 0 0 0 2.112393379 0
120-1980 0 1 0 0 0 0 0 10 0 1 0 0.258554876 0
120-1981 0 1 0 0 0 0 0 10 0 1 0 1.319971681 1
120-1982 0 1 0 0 0 0 0 10 0 1 0 1.462085247 0
120-1983 0 1 0 0 0 0 0 10 0 1 0 1.320286870 0
120-1984 0 1 0 0 0 0 0 10 0 0 0 1.703646541 0
120-1985 0 1 0 0 0 0 0 10 0 1 0 1.445803165 0
120-1986 0 0 0 0 0 0 0 10 0 0 0 1.806364059 0
120-1987 0 0 0 0 0 0 0 10 0 0 0 2.148120165 0
126-1980 0 0 0 0 0 0 0 13 0 1 0 1.737285495 0
126-1981 0 0 0 0 0 0 0 13 0 1 0 1.989600897 1
126-1982 0 0 0 0 0 0 0 13 0 1 0 2.189916849 0
126-1983 0 0 0 0 0 0 0 13 0 1 0 1.855463266 0
126-1984 0 0 0 0 0 0 0 13 0 1 0 1.922437787 0
126-1985 0 0 0 0 0 0 0 13 0 1 0 2.061023951 0
126-1986 0 0 0 0 0 0 0 13 0 1 0 1.782201648 0
126-1987 0 0 0 0 0 0 0 13 0 1 0 2.414681673 0
150-1980 0 0 0 0 0 0 0 12 0 0 0 1.208735347 0
150-1981 0 0 0 0 0 0 0 12 0 0 0 1.194039702 1
150-1982 0 0 0 0 0 0 0 12 0 0 0 1.170440555 0
150-1983 0 0 0 0 0 0 0 12 0 0 0 1.097964525 0
150-1984 0 1 0 0 0 0 0 12 0 0 0 0.765816212 0
150-1985 0 1 0 0 0 0 0 12 0 0 0 1.119025946 0
150-1986 0 0 0 0 0 0 0 12 0 0 0 1.119366765 0
150-1987 0 1 0 0 0 0 0 12 0 0 1 0.831459522 0
162-1980 0 0 0 0 0 0 0 11 0 1 1 0.502470136 0
162-1981 0 0 0 1 0 0 0 11 0 0 0 1.064912319 1
162-1982 0 0 0 0 0 0 0 11 0 0 0 1.189497948 0
162-1983 0 0 0 0 0 0 0 11 0 1 0 1.539888501 0
162-1984 0 0 0 1 0 0 0 11 0 0 0 1.598286033 0
162-1985 0 0 0 0 0 0 0 11 0 1 0 1.737320662 0
162-1986 0 0 0 0 0 0 0 11 0 1 0 1.988455892 0
162-1987 0 0 0 1 0 0 1 11 0 0 0 2.158678532 0
166-1980 0 0 0 0 0 0 0 10 0 1 1 1.005293965 0
166-1981 0 0 0 0 0 0 0 10 0 1 1 0.937687397 1
166-1982 0 0 0 0 0 0 0 10 0 1 1 1.367487669 0
166-1983 0 0 0 0 0 0 0 10 0 1 1 1.378008723 0
166-1984 0 0 0 0 0 0 0 10 0 1 1 1.170183539 0
166-1985 0 0 0 0 0 0 0 10 0 1 0 1.728221416 0
166-1986 0 0 0 0 0 0 0 10 0 1 0 1.709864736 0
166-1987 0 0 0 0 0 1 0 10 0 1 0 1.851074815 0
189-1980 0 0 0 0 0 0 0 14 0 1 0 1.130545378 0
189-1981 0 0 0 0 0 0 0 14 0 1 0 0.836248040 1
189-1982 0 0 0 0 0 0 0 14 0 1 0 1.467359781 0
189-1983 0 0 0 0 0 0 0 14 0 1 0 1.071483612 0
189-1984 0 0 0 0 0 0 0 14 0 1 0 1.445919514 0
189-1985 0 0 0 0 0 0 0 14 0 1 0 1.685116291 0
189-1986 0 0 0 0 0 0 0 14 0 0 0 1.686174989 0
189-1987 0 0 0 0 0 0 0 14 0 0 0 1.755130291 0
193-1980 0 0 0 0 0 0 0 14 0 0 0 1.565691948 0
193-1981 0 0 0 0 0 0 0 14 0 0 0 2.493875265 1
193-1982 0 0 0 0 0 0 0 14 0 0 0 1.822662115 0
193-1983 0 0 0 0 0 0 0 14 0 0 0 2.380336046 0
193-1984 0 0 0 0 0 0 0 14 0 0 0 2.217128515 0
193-1985 0 0 0 0 0 0 0 14 0 0 0 2.272031546 0
193-1986 0 0 0 0 0 0 0 14 0 0 0 2.353798628 0
193-1987 0 0 0 0 0 0 0 14 0 0 0 2.429450035 0
209-1980 0 1 0 0 0 0 0 11 0 1 0 1.918003201 0
209-1981 0 1 0 0 0 0 0 11 0 1 0 0.765407741 1
209-1982 0 1 0 0 0 0 0 11 0 1 0 1.978185415 0
209-1983 0 1 0 0 0 0 0 11 0 1 0 1.948553681 0
209-1984 0 1 0 0 0 0 0 11 0 0 0 2.037025928 0
209-1985 0 0 0 0 0 0 0 11 0 1 0 1.902574778 0
209-1986 0 0 0 0 0 0 0 11 0 1 0 1.972603679 0
209-1987 0 0 0 0 0 0 0 11 0 0 0 2.186982155 0
212-1980 0 0 0 0 0 0 0 11 0 0 0 1.784471750 0
212-1981 0 0 0 0 0 0 0 11 0 0 0 2.179982662 1
212-1982 0 0 0 0 0 0 0 11 0 0 1 1.963865399 0
212-1983 0 0 0 0 0 0 0 11 0 0 0 2.044932842 0
212-1984 0 0 0 0 0 0 0 11 0 0 0 2.012861252 0
212-1985 0 0 0 0 0 0 0 11 0 0 0 2.096985817 0
212-1986 0 0 0 0 0 0 0 11 0 0 0 2.143966198 0
212-1987 0 0 0 0 0 0 0 11 0 0 1 2.241284370 0
218-1980 0 0 0 1 0 0 0 15 0 0 0 2.013313293 0
218-1981 0 0 0 1 0 0 0 15 0 0 0 1.962152481 1
218-1982 0 0 0 1 0 0 0 15 0 0 0 2.275640965 0
218-1983 0 0 0 0 0 0 0 15 0 0 0 2.194917679 0
218-1984 0 0 0 1 0 0 0 15 0 0 0 2.428337336 0
218-1985 0 0 0 0 0 0 0 15 0 0 0 2.723037004 0
218-1986 0 0 0 0 0 0 0 15 0 0 0 2.966396332 0
218-1987 0 0 0 0 0 0 0 15 0 0 0 3.065051794 0
243-1980 0 0 0 0 0 0 0 12 1 0 0 1.564181328 0
243-1981 0 0 0 0 0 0 0 12 1 0 0 1.683545828 1
243-1982 0 0 0 0 1 0 0 12 0 0 0 1.690503359 0
243-1983 0 0 0 0 1 0 0 12 0 0 0 1.660871625 0
243-1984 0 0 0 0 1 0 0 12 0 0 0 1.698050618 0
243-1985 0 0 0 0 1 0 0 12 0 0 0 1.671768188 0
243-1986 0 0 0 0 1 0 0 12 0 0 0 1.635717511 0
243-1987 0 0 0 0 0 0 0 12 1 0 0 1.786970973 0
259-1980 0 0 0 0 0 0 0 12 0 0 1 2.107189655 0
259-1981 0 0 0 0 0 0 0 12 0 0 1 2.089010954 1
259-1982 0 0 0 0 0 0 0 12 0 0 1 2.042723894 0
259-1983 0 0 0 0 0 0 0 12 0 0 1 1.308155775 0
259-1984 0 0 0 0 0 0 0 12 0 0 0 1.488152266 0
259-1985 0 0 0 0 0 0 0 12 0 0 0 1.542818189 0
259-1986 0 0 0 0 0 0 0 12 0 1 0 1.535134673 0
259-1987 0 0 0 0 0 0 0 12 0 1 0 1.454335570 0
260-1980 0 0 0 0 0 0 0 11 0 1 1 1.629912019 0
260-1981 0 0 0 0 0 0 0 11 0 1 1 1.775113106 1
260-1982 0 0 0 0 0 0 0 11 0 0 0 1.967256308 0
260-1983 0 0 0 0 0 0 0 11 0 0 0 2.075186253 0
260-1984 0 0 0 0 0 0 0 11 0 0 0 2.128833532 0
260-1985 0 0 0 0 0 0 0 11 0 0 0 2.268419266 0
260-1986 0 0 0 0 0 0 0 11 0 0 0 1.992139101 0
260-1987 0 0 0 0 0 0 0 11 0 0 0 2.421554565 0
309-1980 0 0 0 0 0 1 0 12 0 0 0 1.786075711 0
309-1981 0 0 0 0 0 0 0 12 0 0 0 2.280766010 1
309-1982 0 0 0 0 0 0 0 12 0 0 0 2.264266253 0
309-1983 0 0 0 0 0 0 0 12 0 0 0 2.275456429 0
309-1984 0 0 0 0 0 0 0 12 0 0 0 2.208132505 0
309-1985 0 0 0 0 0 0 0 12 0 0 0 2.199852467 0
309-1986 0 0 0 0 0 0 0 12 0 0 0 2.206899881 0
309-1987 0 0 0 0 0 0 0 12 0 0 0 2.476866961 0
351-1980 0 0 0 0 0 0 0 12 0 0 0 1.643386841 0
351-1981 0 0 0 0 0 0 0 12 0 0 0 1.335580468 1
351-1982 0 0 0 0 0 0 0 12 0 0 0 1.522817850 0
351-1983 0 0 0 0 0 0 0 12 0 0 0 1.418851376 0
351-1984 0 0 0 0 0 0 0 12 0 0 0 0.903927445 0
351-1985 0 0 0 0 0 0 0 12 1 0 0 1.888564110 0
351-1986 0 0 0 1 0 0 0 12 0 0 0 1.783449650 0
351-1987 0 0 0 1 0 0 0 12 0 0 0 1.698008299 0
353-1980 0 0 0 0 0 0 0 12 0 0 0 1.838197231 0
353-1981 0 0 0 0 0 0 0 12 0 0 1 1.817077279 1
353-1982 0 0 0 0 0 0 0 12 0 1 0 1.671740294 0
353-1983 0 0 0 0 0 0 0 12 0 0 0 1.572830558 0
353-1984 0 0 0 0 0 0 0 12 0 0 0 1.682546377 0
353-1985 0 0 0 0 0 0 0 12 0 0 0 1.583640218 0
353-1986 0 0 0 0 0 0 0 12 0 0 0 1.773293138 0
353-1987 0 0 0 0 0 0 0 12 0 0 0 1.861078978 0
383-1980 0 0 0 0 0 0 0 12 0 0 0 1.462888122 0
383-1981 0 0 0 0 0 0 0 12 0 0 0 1.570217252 1
383-1982 0 0 0 0 0 0 0 12 0 0 1 1.656601787 0
383-1983 0 0 0 0 0 0 0 12 0 0 0 1.725410104 0
383-1984 0 0 0 0 0 0 0 12 0 0 0 1.772158504 0
383-1985 0 0 0 0 0 0 0 12 0 0 0 2.011084318 0
383-1986 0 0 0 0 0 0 0 12 0 0 0 1.991016626 0
383-1987 0 0 0 0 0 0 0 12 0 0 0 1.952050686 0
408-1980 0 0 0 0 0 0 0 11 0 0 0 1.652094960 0
408-1981 0 0 0 0 0 0 0 11 0 0 0 1.489534974 1
408-1982 0 0 0 0 0 0 0 11 0 0 0 1.881175756 0
408-1983 0 0 0 0 0 0 0 11 0 0 0 2.061031580 0
408-1984 0 0 0 0 0 0 0 11 0 0 1 2.488836288 0
408-1985 0 0 0 0 0 0 0 11 0 0 1 2.430938005 0
408-1986 0 0 0 0 0 0 0 11 0 0 1 2.534560442 0
408-1987 0 0 0 0 0 0 0 11 0 0 1 2.069602489 0
424-1980 0 0 0 0 0 0 0 12 0 0 0 2.165839434 0
424-1981 0 0 0 0 0 0 0 12 0 0 0 2.325399876 1
424-1982 0 0 0 0 0 0 0 12 0 0 0 2.383650541 0
424-1983 0 0 0 0 0 0 0 12 0 0 0 2.337211609 0
424-1984 0 0 0 0 0 0 0 12 0 0 0 2.412507534 0
424-1985 0 0 0 0 0 0 0 12 0 0 0 2.384145975 0
424-1986 0 0 0 0 0 0 0 12 0 0 0 2.352030039 0
424-1987 0 0 0 0 0 0 0 12 0 0 0 2.577756643 0
464-1980 0 0 0 0 0 0 0 13 0 1 0 0.972626269 0
464-1981 0 0 0 0 0 0 0 13 0 1 0 1.003104448 1
464-1982 0 0 0 0 0 0 0 13 0 1 0 1.099635005 0
464-1983 0 0 0 0 0 0 0 13 0 1 0 1.214584470 0
464-1984 0 0 0 0 0 0 0 13 0 1 0 1.319241762 0
464-1985 0 0 0 0 0 0 0 13 0 1 0 1.389742494 0
464-1986 0 0 0 0 0 0 0 13 0 1 0 1.573538065 0
464-1987 0 0 0 0 0 0 0 13 0 1 0 1.900699735 0
483-1980 0 0 0 0 0 0 0 12 0 0 0 1.682627082 0
483-1981 0 0 0 0 0 0 0 12 0 0 0 1.661706328 1
483-1982 0 0 0 0 0 0 0 12 0 0 0 1.755041838 0
483-1983 0 0 0 0 0 0 0 12 0 0 1 1.753450751 0
483-1984 0 0 0 0 0 0 0 12 0 0 0 1.618007898 0
483-1985 0 0 0 0 0 0 0 12 0 0 0 1.648178697 0
483-1986 0 0 0 0 0 0 0 12 0 0 0 1.745894194 0
483-1987 0 0 0 0 0 0 0 12 0 0 0 1.727081895 0
556-1980 0 1 0 0 0 0 0 14 0 1 0 1.939345479 0
556-1981 0 0 0 0 0 0 0 14 1 0 0 2.120263577 1
556-1982 0 0 0 0 0 0 0 14 1 0 0 2.160506964 0
556-1983 0 0 0 0 0 0 0 14 1 0 0 2.489253998 0
556-1984 0 0 0 0 0 0 0 14 1 0 0 2.375693560 0
556-1985 0 0 0 0 0 0 0 14 1 0 0 2.295886755 0
556-1986 0 0 0 0 0 0 0 14 1 0 0 2.299090147 0
556-1987 0 0 0 0 0 0 0 14 1 0 0 2.581879377 0
560-1980 0 1 0 0 0 0 0 12 1 0 0 1.386847258 0
560-1981 0 1 0 0 0 0 0 12 1 0 0 2.127581835 1
560-1982 0 1 0 0 0 0 0 12 1 0 0 0.968870223 0
560-1983 0 0 0 0 0 0 0 12 0 1 0 1.163598895 0
560-1984 0 0 0 0 0 0 0 12 0 0 0 1.356619120 0
560-1985 0 0 0 0 0 0 0 12 0 0 0 1.416253328 0
560-1986 0 0 0 0 0 0 0 12 1 0 1 1.214983225 0
560-1987 0 0 0 0 0 0 0 12 0 0 0 1.639359474 0
569-1980 0 0 0 0 0 0 0 12 0 1 0 0.683725059 0
569-1981 0 0 0 0 0 0 0 12 0 1 0 1.078989029 1
569-1982 0 0 0 0 0 0 0 12 0 1 0 0.839635730 0
569-1983 0 0 0 0 0 0 0 12 0 1 0 1.507569075 0
569-1984 0 0 0 0 0 0 0 12 0 0 0 1.020651698 0
569-1985 0 0 0 0 0 0 0 12 0 1 0 0.542597771 0
569-1986 0 0 0 0 0 0 0 12 0 1 0 0.114716314 0
569-1987 0 0 0 0 0 0 0 12 0 1 0 0.312851757 0
583-1980 0 0 0 0 0 0 0 12 0 1 0 1.626772165 0
583-1981 0 0 0 0 0 0 0 12 0 0 0 1.880874991 1
583-1982 0 0 0 0 0 0 0 12 0 0 1 1.741196513 0
583-1983 0 0 0 0 0 0 0 12 0 0 1 2.194788456 0
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583-1985 0 0 0 0 0 0 0 12 0 0 0 1.918448210 0
583-1986 0 0 0 0 0 0 0 12 0 0 0 2.156713724 0
583-1987 0 0 0 0 0 0 0 12 0 0 0 1.985040903 0
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647-1981 0 0 0 0 0 0 0 12 0 0 1 1.519825697 1
647-1982 0 0 0 0 0 0 0 12 0 0 1 1.509153008 0
647-1983 0 0 0 0 0 0 0 12 0 0 1 1.645041585 0
647-1984 0 0 0 0 0 0 0 12 0 0 1 1.549015045 0
647-1985 0 0 0 0 0 0 0 12 0 0 1 1.826956272 0
647-1986 0 0 0 0 1 0 0 12 0 0 1 1.883680344 0
647-1987 0 0 0 0 1 0 0 12 0 0 1 2.023660660 0
658-1980 0 0 0 0 0 0 0 12 0 0 1 1.731417298 0
658-1981 0 0 0 0 0 0 0 12 0 0 0 1.813758969 1
658-1982 0 0 0 0 0 0 0 12 0 0 1 1.700048327 0
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658-1985 0 0 0 0 0 0 0 12 0 0 0 2.099785089 0
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684-1981 0 0 0 0 0 0 0 12 0 0 0 2.179982662 1
684-1982 0 0 0 0 0 0 0 12 0 0 0 2.309426546 0
684-1983 0 0 0 0 0 0 0 12 0 0 0 2.251321316 0
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684-1985 0 0 0 0 0 0 0 12 0 0 0 2.313848257 0
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684-1987 0 0 0 0 0 0 0 12 0 1 0 2.405352592 0
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711-1981 0 0 0 0 0 0 0 11 0 1 0 1.366491675 1
711-1982 0 0 0 0 0 0 0 11 0 1 0 1.690503359 0
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729-1982 0 0 0 0 0 1 0 13 0 0 1 3.096215725 0
729-1983 0 0 0 0 0 1 0 13 0 0 1 1.910813332 0
729-1984 0 0 0 0 0 0 0 13 0 0 0 1.615264416 0
729-1985 0 0 0 0 0 0 0 13 0 0 0 2.076528072 0
729-1986 0 0 0 0 0 0 0 13 0 1 0 2.107539892 0
729-1987 0 0 0 0 0 0 0 13 0 0 0 2.155585289 0
731-1980 0 0 0 0 0 1 0 12 0 1 0 1.655638933 0
731-1981 1 0 0 0 0 1 0 12 0 0 0 1.464255929 1
731-1982 1 0 0 0 0 1 0 12 0 0 0 1.007827520 0
731-1983 0 1 0 0 0 1 0 12 0 0 0 1.477949262 0
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731-1986 0 1 1 0 0 1 0 12 0 0 0 2.657730579 0
731-1987 0 0 0 0 0 1 0 12 0 0 0 2.139191628 0
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732-1981 0 0 0 0 0 1 0 12 0 0 0 1.601715922 1
732-1982 0 0 0 0 0 1 0 12 0 0 0 1.504842877 0
732-1983 0 0 0 0 0 1 0 12 0 0 0 1.798046827 0
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793-1981 0 1 1 0 0 0 0 14 0 0 0 1.931021571 1
793-1982 0 1 0 0 0 0 0 14 0 1 0 1.902649879 0
793-1983 0 1 1 0 0 0 0 14 0 0 0 1.885374784 0
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1316-1986 0 0 0 0 0 0 1 8 0 0 0 1.911142111 0
1316-1987 0 0 0 0 0 1 1 8 0 1 0 1.907598972 0
1318-1980 0 0 0 0 0 1 1 8 0 0 0 1.059776306 0
1318-1981 0 0 0 0 0 1 1 8 0 0 0 1.467701674 1
1318-1982 1 0 0 0 0 1 1 8 0 0 0 1.339763165 0
1318-1983 1 0 0 0 0 1 1 8 0 0 0 1.294627190 0
1318-1984 0 0 0 0 0 1 0 8 0 0 0 1.251763463 0
1318-1985 1 0 0 0 0 1 1 8 0 0 0 1.332202554 0
1318-1986 0 0 0 0 0 1 1 8 0 0 0 1.285940886 0
1318-1987 0 0 0 0 0 1 1 8 0 0 0 1.286195636 0
1345-1980 0 0 0 0 0 0 1 12 0 0 0 1.764698148 0
1345-1981 0 0 0 0 0 0 1 12 0 1 0 -0.723918855 1
1345-1982 0 0 0 0 0 0 1 12 0 0 0 1.890843391 0
1345-1983 0 0 0 0 0 0 1 12 0 1 0 2.088315487 0
1345-1984 0 0 0 0 0 0 1 12 0 0 0 2.206275463 0
1345-1985 0 0 0 0 0 0 1 12 0 0 0 2.159004450 0
1345-1986 0 0 0 0 0 0 1 12 0 1 0 2.221297026 0
1345-1987 0 0 0 0 0 0 1 12 0 1 0 1.583854198 0
1397-1980 0 0 0 0 0 0 1 12 0 0 1 1.770083070 0
1397-1981 0 0 0 0 0 0 1 12 0 0 1 1.601715922 1
1397-1982 0 0 0 0 0 0 1 12 0 0 1 1.547402501 0
1397-1983 0 0 0 0 0 0 1 12 0 0 1 1.786034703 0
1397-1984 0 0 0 0 0 0 1 12 0 0 1 1.682546377 0
1397-1985 0 0 0 0 0 0 1 12 0 0 1 1.720499396 0
1397-1986 0 0 0 0 0 0 1 12 0 0 1 1.799961448 0
1397-1987 0 0 0 0 0 0 1 12 0 0 1 1.760995507 0
1434-1980 0 0 0 0 0 0 1 10 0 0 0 0.206286430 0
1434-1981 0 0 0 0 0 0 1 10 0 0 0 1.121049643 1
1434-1982 0 1 0 1 0 0 1 10 0 0 1 1.086117387 0
1434-1983 0 1 0 1 0 0 1 10 0 0 1 1.268914819 0
1434-1984 0 1 0 0 0 0 1 10 0 0 1 1.099372625 0
1434-1985 0 0 0 0 0 0 1 10 0 1 1 1.345229149 0
1434-1986 0 1 0 0 0 0 1 10 0 0 0 1.900044918 0
1434-1987 0 1 0 1 0 0 1 10 0 0 0 1.515391827 0
1492-1980 0 0 0 0 0 1 1 13 0 0 0 2.036455393 0
1492-1981 0 0 0 0 0 0 1 13 0 1 0 1.142368317 1
1492-1982 0 0 0 0 0 0 1 13 1 0 0 1.378535867 0
1492-1983 0 0 0 0 0 0 1 13 1 0 0 1.473753810 0
1492-1984 0 0 0 0 0 0 1 13 0 0 0 1.474907041 0
1492-1985 0 0 0 0 0 0 1 13 0 0 0 1.416282415 0
1492-1986 0 0 0 0 0 0 1 13 0 0 0 1.498433352 0
1492-1987 0 0 0 0 0 0 1 13 0 0 0 1.500852585 0
1496-1980 0 1 0 0 0 1 1 12 0 1 1 1.178336024 0
1496-1981 0 1 0 0 0 1 1 12 0 1 1 1.087287188 1
1496-1982 0 0 0 0 0 1 1 12 0 1 0 0.007734179 0
1496-1983 0 0 0 0 0 0 1 12 0 1 0 0.796704948 0
1496-1984 0 0 1 0 0 0 1 12 0 0 0 1.037228346 0
1496-1985 0 0 1 0 0 0 1 12 0 0 0 1.208374143 0
1496-1986 0 0 0 0 0 0 1 12 0 1 0 1.204458833 0
1496-1987 0 0 0 0 0 0 1 12 1 0 0 1.857080460 0
1506-1980 0 0 0 0 0 0 1 12 0 0 0 0.974396646 0
1506-1981 0 0 0 0 0 0 1 12 0 0 0 2.465104103 1
1506-1982 0 0 0 0 0 0 1 12 0 1 0 1.055035710 0
1506-1983 0 1 0 0 0 0 1 12 0 1 0 1.142764807 0
1506-1984 0 0 0 0 0 0 1 12 0 1 0 1.012746572 0
1506-1985 0 0 0 0 0 0 1 12 0 1 0 1.072814584 0
1506-1986 0 0 0 0 0 0 1 12 0 1 0 1.059984684 0
1506-1987 0 0 0 0 0 0 1 12 0 0 0 0.926926672 0
1515-1980 0 0 0 0 0 0 1 10 0 1 0 1.033779383 0
1515-1981 0 0 0 0 0 0 1 10 0 1 1 1.292640924 1
1515-1982 0 0 0 0 0 0 1 10 0 1 0 1.314466357 0
1515-1983 0 0 0 0 0 0 1 10 0 1 0 1.258214831 0
1515-1984 0 0 0 0 0 0 1 10 1 0 0 1.647278190 0
1515-1985 0 0 0 0 0 0 1 10 1 0 0 1.765961766 0
1515-1986 0 0 0 0 0 0 1 10 1 0 0 1.799961448 0
1515-1987 0 0 0 0 0 1 1 10 1 0 0 1.810687423 0
1520-1980 0 0 0 0 0 0 1 12 0 0 1 1.375922918 0
1520-1981 1 0 0 0 0 0 1 12 0 0 1 1.353907824 1
1520-1982 0 0 0 0 0 0 1 12 0 0 0 1.349576831 0
1520-1983 0 0 0 0 0 0 1 12 0 0 0 1.351197481 0
1520-1984 0 0 0 0 0 0 1 12 0 0 0 1.370305777 0
1520-1985 0 0 0 0 0 0 1 12 0 0 0 1.401318669 0
1520-1986 0 0 0 0 0 0 1 12 0 0 0 1.580542803 0
1520-1987 0 0 0 0 0 0 1 12 0 1 1 1.635994911 0
1528-1980 0 1 0 0 0 0 1 10 0 1 1 0.978897810 0
1528-1981 0 1 0 0 0 0 1 10 0 1 0 1.241713166 1
1528-1982 0 1 0 0 0 0 1 10 0 1 0 1.259720445 0
1528-1983 0 1 0 0 0 0 1 10 0 1 0 1.032262921 0
1528-1984 0 1 0 0 0 0 1 10 0 1 0 1.196193576 0
1528-1985 0 1 0 0 0 0 1 10 0 1 0 1.168104529 0
1528-1986 0 1 0 0 0 0 1 10 0 1 0 1.366404533 0
1528-1987 0 1 0 1 0 0 0 10 0 0 0 1.398312926 0
1554-1980 0 0 0 0 0 0 1 12 0 0 0 1.311867356 0
1554-1981 0 0 0 0 0 0 1 12 0 1 0 1.222664952 1
1554-1982 0 0 0 0 0 0 1 12 0 0 1 1.408866644 0
1554-1983 0 0 0 0 0 0 1 12 0 0 0 1.574341059 0
1554-1984 0 0 0 0 0 0 1 12 0 0 0 1.455858827 0
1554-1985 0 0 0 0 0 0 1 12 0 0 0 1.874824882 0
1554-1986 0 0 0 0 0 0 1 12 0 0 0 1.873946190 0
1554-1987 0 0 0 0 0 0 1 12 0 0 0 1.733726382 0
1575-1980 0 0 0 0 0 0 0 13 0 0 0 1.576051474 0
1575-1981 0 0 0 0 0 0 0 13 0 0 0 1.742017388 1
1575-1982 0 0 0 0 0 0 0 13 0 0 0 1.778826833 0
1575-1983 0 0 0 0 0 0 0 13 0 0 0 1.871161580 0
1575-1984 0 0 0 0 0 0 0 13 0 0 0 1.656395555 0
1575-1985 0 0 0 0 0 0 0 13 0 0 0 1.783029675 0
1575-1986 0 0 0 0 0 0 0 13 0 0 0 1.594825149 0
1575-1987 0 0 0 0 0 0 0 13 0 0 0 1.995091200 0
1576-1980 0 0 0 0 0 0 0 11 0 0 0 1.324701309 0
1576-1981 0 1 0 0 0 0 0 11 0 0 0 1.347073674 1
1576-1982 0 1 1 0 0 0 0 11 0 0 0 1.562669992 0
1576-1983 0 1 1 0 0 0 0 11 0 0 0 3.200689077 0
1576-1984 0 0 0 0 0 0 0 11 0 0 0 1.838300943 0
1576-1985 0 0 0 0 0 0 1 11 0 0 0 1.870448589 0
1576-1986 0 0 0 0 0 0 0 11 0 0 0 0.825764716 0
1576-1987 0 0 0 0 0 0 0 11 0 0 0 1.844714403 0
1628-1980 0 0 0 0 0 0 0 12 0 1 0 1.176472902 0
1628-1981 0 0 0 0 0 0 0 12 0 1 0 1.324258924 1
1628-1982 0 0 0 0 0 0 0 12 0 0 0 1.235966325 0
1628-1983 0 0 0 0 0 0 0 12 0 1 0 1.592994094 0
1628-1984 0 1 0 0 1 0 0 12 0 0 0 1.725366354 0
1628-1985 0 1 0 0 1 0 0 12 0 0 0 1.820029020 0
1628-1986 0 1 0 0 1 0 0 12 0 0 0 1.836141109 0
1628-1987 0 0 0 0 1 0 0 12 0 0 0 1.861078978 0
1641-1980 0 0 0 0 0 0 0 12 0 1 0 2.111690521 0
1641-1981 0 0 0 0 0 0 0 12 0 1 0 2.170552254 1
1641-1982 0 0 0 0 0 0 0 12 0 1 0 2.134839296 0
1641-1983 0 0 0 0 0 0 0 12 0 1 0 2.072430134 0
1641-1984 0 0 0 0 0 0 0 12 0 1 0 2.040540934 0
1641-1985 0 0 0 0 0 0 0 12 0 1 0 2.018958330 0
1641-1986 0 0 0 0 0 0 0 12 0 1 0 2.167382479 0
1641-1987 0 0 0 0 0 0 0 12 0 0 0 1.873488426 0
1644-1980 0 0 0 0 0 0 0 12 0 0 1 0.560979187 0
1644-1981 0 0 0 0 0 0 0 12 0 0 0 1.546365261 1
1644-1982 0 0 0 0 0 0 0 12 0 0 0 1.531898379 0
1644-1983 0 0 0 0 0 0 0 12 0 0 0 1.591878653 0
1644-1984 0 0 0 0 0 0 0 12 0 0 0 1.685167909 0
1644-1985 0 0 0 0 0 0 0 12 0 0 0 1.648178697 0
1644-1986 0 0 0 0 0 0 0 12 0 0 0 1.565979362 0
1644-1987 0 0 0 0 0 0 0 12 0 0 0 2.068422556 0
1653-1980 0 0 0 0 0 0 0 15 0 1 1 -0.384581894 0
1653-1981 0 0 0 0 0 0 0 15 0 1 1 1.886070132 1
1653-1982 0 0 0 0 0 0 0 15 0 1 1 1.987385154 0
1653-1983 0 0 0 0 0 0 0 15 0 1 1 2.136661053 0
1653-1984 0 0 0 0 0 0 0 15 0 1 1 1.804233789 0
1653-1985 0 0 0 0 0 0 0 15 0 0 0 2.130121469 0
1653-1986 0 0 0 0 0 0 0 15 0 0 0 2.631413221 0
1653-1987 0 0 0 0 0 0 0 15 0 0 0 2.793118000 0
1654-1980 0 0 0 0 0 0 0 11 0 0 0 1.624841690 0
1654-1981 0 0 0 0 0 0 0 11 0 0 0 1.616872907 1
1654-1982 0 0 0 0 0 0 0 11 0 0 0 1.429619431 0
1654-1983 0 0 0 0 0 0 0 11 0 0 0 1.736459970 0
1654-1984 0 0 0 0 0 0 0 11 0 0 0 1.716041565 0
1654-1985 0 0 0 0 0 0 0 11 0 0 0 1.809021235 0
1654-1986 0 0 0 0 0 0 0 11 0 0 0 1.799961448 0
1654-1987 0 0 0 0 0 0 0 11 0 0 0 2.183852434 0
1721-1980 0 0 0 0 0 0 0 11 0 1 0 1.784471750 0
1721-1981 0 0 0 0 0 0 0 11 0 1 1 1.934860349 1
1721-1982 0 0 0 0 0 0 0 11 0 1 0 2.026975632 0
1721-1983 0 0 0 0 0 0 0 11 0 1 0 2.109821796 0
1721-1984 0 0 0 0 0 0 0 11 0 1 0 2.128833532 0
1721-1985 0 0 0 0 0 0 0 11 0 1 1 2.094465733 0
1721-1986 0 0 0 0 0 0 0 11 0 1 0 2.256719828 0
1721-1987 0 0 0 0 0 0 0 11 0 0 0 2.910901070 0
1742-1980 0 0 0 0 0 0 0 12 1 0 1 1.461624742 0
1742-1981 0 0 0 0 0 0 0 12 1 0 1 1.682905078 1
1742-1982 0 0 0 0 0 0 0 12 0 0 0 1.872824907 0
1742-1983 0 0 0 0 0 0 0 12 0 0 0 2.043863773 0
1742-1984 0 0 0 0 0 0 0 12 0 0 0 2.350375652 0
1742-1985 0 0 0 0 0 0 0 12 0 1 0 2.387135506 0
1742-1986 0 0 0 0 0 0 0 12 0 0 0 2.410870552 0
1742-1987 0 0 0 0 0 0 0 12 0 0 0 2.480118036 0
1744-1980 0 0 0 0 0 0 0 11 0 0 1 1.630321145 0
1744-1981 0 0 0 0 0 0 0 11 0 0 1 1.683545828 1
1744-1982 0 0 0 0 0 0 0 11 0 0 1 1.781017423 0
1744-1983 0 0 0 0 0 0 0 11 0 0 1 1.381638527 0
1744-1984 0 0 0 0 0 0 0 11 0 1 1 2.030624151 0
1744-1985 0 0 0 0 0 0 0 11 0 1 1 1.810697675 0
1744-1986 0 1 0 0 0 0 0 11 0 0 1 2.012397528 0
1744-1987 0 0 0 0 0 0 0 11 0 0 1 2.320032835 0
1763-1980 0 0 1 0 0 0 0 11 0 0 0 0.643500268 0
1763-1981 0 1 0 0 0 0 0 11 0 1 0 0.897941589 1
1763-1982 0 1 0 0 0 0 0 11 0 1 1 1.278796554 0
1763-1983 0 1 0 0 0 0 0 11 0 1 1 1.335449219 0
1763-1984 0 1 0 0 0 0 0 11 0 1 0 1.526200294 0
1763-1985 0 1 0 0 0 0 0 11 0 1 0 1.434203506 0
1763-1986 0 1 0 0 0 0 0 11 0 1 0 0.060374726 0
1763-1987 0 1 0 0 0 0 0 11 0 1 0 1.393775940 0
1777-1980 0 0 0 0 0 0 0 15 0 1 0 1.389388084 0
1777-1981 0 0 0 1 0 0 0 15 0 0 0 1.241713166 1
1777-1982 0 0 0 1 0 0 0 15 0 0 0 0.985908806 0
1777-1983 0 0 0 1 0 0 0 15 0 0 0 1.144054294 0
1777-1984 0 0 0 0 0 0 0 15 1 0 0 1.654600501 0
1777-1985 0 0 0 1 0 0 0 15 0 0 1 1.648178697 0
1777-1986 0 0 0 1 0 0 0 15 0 0 1 1.333059907 0
1777-1987 0 1 0 1 0 0 0 15 0 0 0 1.738180757 0
1843-1980 0 0 0 0 0 0 0 15 0 0 0 2.364290237 0
1843-1981 0 0 0 0 0 0 0 15 0 0 0 2.337618113 1
1843-1982 0 0 0 0 0 0 0 15 0 0 0 2.416440487 0
1843-1983 0 0 0 0 0 0 0 15 0 0 0 2.513867378 0
1843-1984 0 0 0 0 0 0 0 15 0 0 0 2.647627354 0
1843-1985 0 0 0 0 0 0 0 15 0 0 0 2.636213303 0
1843-1986 0 0 0 0 0 0 0 15 0 0 0 2.718755245 0
1843-1987 0 0 0 0 0 0 0 15 0 0 0 2.768743992 0
1891-1980 0 0 0 0 0 0 0 12 0 1 1 0.937173963 0
1891-1981 0 0 0 0 0 0 0 12 0 1 0 1.018830419 1
1891-1982 0 0 0 0 0 0 0 12 0 0 0 1.119958520 0
1891-1983 0 1 0 0 0 1 0 12 0 1 0 0.838389754 0
1891-1984 0 1 0 0 0 1 0 12 0 1 0 1.246248245 0
1891-1985 0 1 0 0 0 1 0 12 0 1 0 1.197977781 0
1891-1986 0 1 0 0 0 1 0 12 0 1 0 1.253417730 0
1891-1987 0 1 0 0 0 1 0 12 0 1 0 1.301463127 0
1895-1980 0 0 0 0 0 0 0 13 0 1 0 1.654456258 0
1895-1981 0 0 0 0 0 0 0 13 0 1 0 1.589547753 1
1895-1982 0 1 0 0 1 0 0 13 0 0 1 1.748772264 0
1895-1983 0 1 0 0 1 0 0 13 0 0 1 1.870592117 0
1895-1984 0 1 0 0 0 0 0 13 0 0 1 2.054110050 0
1895-1985 0 1 0 0 1 0 0 13 0 0 1 1.903898478 0
1895-1986 0 1 0 0 1 0 0 13 0 0 1 2.083877087 0
1895-1987 0 1 0 0 1 1 0 13 0 0 1 2.282292366 0
1899-1980 0 0 0 0 0 0 0 12 0 0 0 1.447999597 0
1899-1981 0 0 0 0 0 0 0 12 0 0 0 1.241713166 1
1899-1982 0 0 0 0 0 0 0 12 0 0 0 1.380348444 0
1899-1983 0 0 0 0 0 1 0 12 0 0 0 0.980969608 0
1899-1984 0 0 0 0 0 1 0 12 0 0 0 1.394864321 0
1899-1985 0 0 0 0 0 1 0 12 0 0 0 1.401318669 0
1899-1986 0 0 0 0 0 1 0 12 0 0 0 1.494579792 0
1899-1987 0 0 0 0 0 1 0 12 0 1 0 1.362457633 0
1925-1980 0 0 0 0 0 1 0 11 0 1 0 1.005991101 0
1925-1981 0 0 0 0 0 1 0 11 0 1 0 1.637409568 1
1925-1982 0 0 0 0 0 1 0 11 0 0 0 1.570719123 0
1925-1983 0 0 0 0 0 1 0 11 0 0 0 1.757986307 0
1925-1984 0 0 0 0 0 1 0 11 0 0 0 1.903860092 0
1925-1985 0 0 0 0 0 1 0 11 0 0 0 1.833581924 0
1925-1986 0 0 0 0 0 1 0 11 0 0 0 1.985459089 0
1925-1987 0 0 0 0 0 1 0 11 0 0 0 1.948571205 0
1930-1980 0 1 0 1 0 0 0 11 0 0 0 1.074007511 0
1930-1981 0 0 0 0 0 1 0 11 0 0 0 0.966762006 1
1930-1982 0 0 0 0 0 1 0 11 0 1 0 1.324258924 0
1930-1983 0 0 0 0 0 1 0 11 0 1 0 0.560657978 0
1930-1984 0 0 0 0 0 1 0 11 0 1 0 1.682546377 0
1930-1985 0 0 0 0 0 1 0 11 0 0 0 1.858743548 0
1930-1986 0 0 0 0 0 1 0 11 0 0 0 1.991016626 0
1930-1987 0 0 0 0 0 0 0 11 0 0 0 2.148761034 0
1961-1980 0 0 0 0 0 1 0 12 0 1 0 1.166015506 0
1961-1981 0 0 0 0 0 1 0 12 0 0 0 1.862028718 1
1961-1982 0 0 0 0 0 0 0 12 0 1 0 1.850352049 0
1961-1983 0 0 0 0 0 0 0 12 0 0 0 1.834120750 0
1961-1984 0 0 0 0 0 0 0 12 0 0 0 1.928381324 0
1961-1985 0 0 0 0 0 0 0 12 0 0 0 1.859849930 0
1961-1986 0 0 0 0 0 1 0 12 0 0 0 2.009258986 0
1961-1987 0 0 0 0 0 1 0 12 0 0 0 2.298619270 0
1963-1980 0 0 0 0 0 1 0 11 0 0 0 1.508624196 0
1963-1981 0 0 0 0 0 1 0 11 0 0 0 1.506138325 1
1963-1982 0 0 0 0 0 1 0 11 0 0 0 1.914808035 0
1963-1983 0 0 0 0 0 1 0 11 0 0 0 1.819908619 0
1963-1984 0 0 0 0 0 1 0 11 0 0 0 1.693128467 0
1963-1985 0 0 0 0 0 1 0 11 0 0 0 1.682080269 0
1963-1986 0 0 0 0 0 1 0 11 0 0 0 1.715822101 0
1963-1987 0 0 0 0 0 1 0 11 0 0 0 1.747149467 0
1979-1980 0 0 0 0 0 0 0 12 0 0 1 2.023541689 0
1979-1981 0 0 0 0 0 0 0 12 0 0 1 2.004293680 1
1979-1982 0 0 0 0 0 0 0 12 0 0 1 1.861060023 0
1979-1983 0 0 0 0 0 0 0 12 0 0 1 2.071156025 0
1979-1984 0 0 0 0 0 0 0 12 0 0 1 1.995276690 0
1979-1985 0 0 0 0 0 0 0 12 0 0 1 1.991968989 0
1979-1986 0 0 0 0 0 0 0 12 0 0 1 2.021503687 0
1979-1987 0 0 0 0 0 0 0 12 0 0 1 1.997938156 0
1988-1980 0 0 0 0 0 0 0 12 0 0 0 -0.247380778 0
1988-1981 0 0 0 0 0 1 0 12 0 0 0 2.283536911 1
1988-1982 0 0 0 0 0 1 0 12 0 0 1 1.294700146 0
1988-1983 0 0 0 0 0 0 0 12 0 0 0 1.150045991 0
1988-1984 0 0 0 0 0 1 0 12 0 0 0 1.571050882 0
1988-1985 0 0 0 0 0 0 0 12 0 0 0 -0.742698967 0
1988-1986 0 0 0 0 0 0 0 12 0 0 0 1.851254702 0
1988-1987 0 0 0 0 0 0 0 12 0 0 0 1.972870350 0
2000-1980 0 0 0 0 0 1 0 11 0 0 1 1.904955506 0
2000-1981 0 0 0 0 0 1 0 11 0 0 0 1.879262328 1
2000-1982 0 0 0 0 0 1 0 11 0 0 1 1.746195674 0
2000-1983 0 0 0 0 0 1 0 11 0 0 0 2.093134880 0
2000-1984 0 0 0 0 0 1 0 11 0 0 0 1.844763756 0
2000-1985 0 0 0 0 0 1 0 11 0 1 0 1.678162217 0
2000-1986 0 0 0 0 0 1 0 11 1 0 0 1.765621901 0
2000-1987 0 0 0 0 0 1 0 11 0 0 1 1.759842277 0
2014-1980 0 0 0 0 0 0 0 12 0 0 1 2.359059334 0
2014-1981 0 0 1 0 0 0 0 12 0 0 0 1.923095465 1
2014-1982 0 0 0 0 0 0 0 12 0 0 0 1.404926896 0
2014-1983 0 0 0 0 0 0 0 12 0 0 0 0.799549878 0
2014-1984 0 0 1 0 0 0 0 12 0 0 0 1.314082265 0
2014-1985 0 0 0 0 0 0 0 12 0 1 0 1.261347771 0
2014-1986 0 0 0 0 0 0 0 12 0 1 0 1.498433352 0
2014-1987 0 0 0 0 0 0 0 12 0 1 0 1.550128579 0
2025-1980 0 0 0 0 0 0 0 13 0 1 0 1.483892441 0
2025-1981 0 1 0 0 0 0 1 13 0 1 0 1.233988643 1
2025-1982 0 0 0 0 0 0 0 13 0 1 0 1.532616496 0
2025-1983 0 0 0 0 0 0 0 13 0 1 0 1.658470631 0
2025-1984 0 0 0 0 0 0 0 13 0 0 0 1.816277623 0
2025-1985 0 0 0 0 0 0 0 13 0 0 0 2.015903473 0
2025-1986 0 0 0 0 0 0 0 13 0 0 0 2.356571913 0
2025-1987 0 0 0 0 0 0 0 13 0 0 1 1.316654921 0
2038-1980 0 1 0 0 0 0 0 10 0 0 0 0.894395828 0
2038-1981 0 1 0 0 0 0 0 10 0 0 0 1.043349624 1
2038-1982 0 1 0 0 0 0 0 10 0 0 0 1.342459679 0
2038-1983 0 1 0 0 0 0 0 10 0 0 0 1.311010599 0
2038-1984 0 1 0 0 0 0 0 10 0 1 0 1.012559056 0
2038-1985 0 0 0 1 0 0 0 10 0 0 0 1.329873800 0
2038-1986 0 0 0 0 0 0 0 10 0 0 0 1.838888049 0
2038-1987 0 0 0 0 0 0 0 10 0 0 0 2.217753887 0
2075-1980 0 0 0 0 0 1 0 12 0 0 1 2.005680323 0
2075-1981 0 0 0 0 0 1 0 12 0 0 1 1.759996533 1
2075-1982 0 0 0 0 0 1 0 12 0 0 1 1.873217463 0
2075-1983 0 0 0 0 0 1 0 12 0 0 0 1.816977262 0
2075-1984 0 0 0 0 0 1 0 12 0 0 0 1.869561195 0
2075-1985 0 0 0 0 0 1 0 12 0 0 0 2.058447123 0
2075-1986 0 0 0 0 0 1 0 12 0 0 0 2.234246969 0
2075-1987 0 0 0 0 0 1 0 12 0 0 0 2.225133896 0
2101-1980 0 0 0 0 0 0 0 12 0 0 0 2.007615328 0
2101-1981 0 0 0 0 0 0 0 12 0 1 0 2.263364315 1
2101-1982 0 0 0 0 0 0 0 12 0 1 0 2.240549803 0
2101-1983 0 0 0 0 0 0 0 12 0 1 1 2.348436594 0
2101-1984 0 0 0 0 0 0 0 12 0 1 0 2.488045216 0
2101-1985 0 0 0 0 0 0 0 12 0 1 1 2.468285561 0
2101-1986 0 0 0 0 0 0 0 12 1 0 1 2.346576214 0
2101-1987 0 0 0 0 0 0 0 12 1 0 0 2.490344763 0
2106-1980 0 0 0 0 0 1 0 12 0 0 1 1.676566482 0
2106-1981 0 0 0 0 0 1 0 12 0 0 1 1.572434306 1
2106-1982 0 0 0 0 0 1 0 12 0 0 1 1.764703751 0
2106-1983 0 0 0 0 0 1 0 12 0 0 1 1.815022230 0
2106-1984 0 0 0 0 0 1 0 12 0 0 1 1.772158504 0
2106-1985 0 0 0 0 0 1 0 12 0 0 1 1.846004486 0
2106-1986 0 0 0 0 0 1 0 12 0 0 1 1.845355034 0
2106-1987 0 0 0 0 0 1 0 12 0 0 1 1.812288761 0
2107-1980 0 0 0 0 0 1 0 10 0 1 0 1.296599865 0
2107-1981 0 0 0 0 0 1 0 10 0 1 0 1.614659905 1
2107-1982 0 0 0 0 0 1 0 10 0 0 1 1.250571251 0
2107-1983 0 0 0 0 0 1 0 10 0 0 1 1.491859317 0
2107-1984 0 1 0 0 1 1 0 10 0 0 0 1.890576243 0
2107-1985 0 1 0 0 1 1 0 10 0 0 0 1.943642974 0
2107-1986 0 1 0 0 1 1 0 10 0 0 0 2.054195642 0
2107-1987 0 1 0 0 1 1 0 10 0 0 0 2.035432339 0
2108-1980 0 0 0 0 0 0 0 12 0 0 0 1.467417598 0
2108-1981 0 0 0 0 0 1 0 12 0 0 1 1.961658478 1
2108-1982 0 0 0 0 0 1 0 12 0 0 1 2.072073460 0
2108-1983 0 0 0 0 0 1 0 12 0 0 1 2.105471134 0
2108-1984 0 0 0 0 0 1 0 12 0 0 1 2.051930904 0
2108-1985 0 0 0 0 0 1 0 12 0 0 1 2.333261251 0
2108-1986 0 0 0 0 0 1 0 12 0 0 1 2.471034288 0
2108-1987 0 0 0 0 0 1 0 12 0 0 1 2.454142570 0
2147-1980 0 1 0 0 0 1 1 11 0 1 0 -0.021080988 0
2147-1981 0 1 0 0 0 1 1 11 0 1 0 -0.148845628 1
2147-1982 0 1 0 0 0 1 1 11 0 1 0 0.180695295 0
2147-1983 0 0 0 0 0 1 1 11 0 1 0 -0.036154479 0
2147-1984 0 0 0 0 0 1 1 11 0 1 0 0.397348136 0
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4128-1983 0 0 0 0 0 0 1 12 0 0 1 1.784833550 0
4128-1984 0 0 0 0 0 0 1 12 0 0 1 1.833685040 0
4128-1985 0 0 0 0 0 0 1 12 0 0 0 1.517054081 0
4128-1986 0 0 0 0 0 0 1 12 0 0 1 1.628111124 0
4128-1987 0 0 0 0 0 0 1 12 0 0 1 1.426626325 0
4159-1980 0 0 0 0 0 0 1 11 1 0 1 1.680458307 0
4159-1981 0 0 0 0 0 0 1 11 1 0 1 2.290006399 1
4159-1982 0 0 0 0 0 0 1 11 0 0 1 2.028579473 0
4159-1983 0 0 0 0 0 0 1 11 1 0 1 1.758648753 0
4159-1984 0 0 0 0 0 0 1 11 1 0 1 2.003092527 0
4159-1985 0 0 0 0 0 0 1 11 0 1 0 1.474594831 0
4159-1986 0 0 0 0 0 0 1 11 0 1 0 2.352030039 0
4159-1987 0 0 0 0 0 0 1 11 0 0 0 1.388474464 0
4204-1980 0 1 1 0 0 0 1 11 0 0 1 1.195795178 0
4204-1981 0 0 0 0 0 0 1 11 1 0 0 1.397355318 1
4204-1982 0 0 0 0 0 0 1 11 0 1 0 1.517894506 0
4204-1983 0 0 0 0 0 0 1 11 0 1 0 1.786034703 0
4204-1984 0 0 0 0 0 0 1 11 0 1 0 1.251763463 0
4204-1985 0 0 0 0 0 0 1 11 1 0 0 1.306227088 0
4204-1986 0 0 0 0 0 0 1 11 0 1 0 1.448196411 0
4204-1987 0 0 0 0 0 0 1 11 0 1 1 1.364976525 0
4229-1980 0 1 0 0 0 0 1 12 0 1 0 1.459483504 0
4229-1981 0 1 0 0 0 0 1 12 0 1 0 1.592908621 1
4229-1982 0 0 0 0 0 0 1 12 0 1 0 1.398366928 0
4229-1983 0 0 0 0 0 0 1 12 0 1 0 1.820720315 0
4229-1984 0 0 0 0 0 0 1 12 0 1 0 1.682546377 0
4229-1985 0 0 0 0 0 0 1 12 0 1 0 1.557775736 0
4229-1986 0 0 0 0 0 0 1 12 0 1 0 1.340429068 0
4229-1987 0 0 0 0 0 0 1 12 0 1 0 1.210274935 0
4258-1980 0 0 0 0 0 0 1 12 0 1 1 2.117404461 0
4258-1981 0 0 0 0 0 0 1 12 0 1 1 2.267192602 1
4258-1982 0 0 0 0 0 0 1 12 0 1 1 1.991294980 0
4258-1983 0 0 0 0 0 0 1 12 0 1 1 2.140562296 0
4258-1984 0 0 0 0 0 0 1 12 0 1 1 2.168054104 0
4258-1985 0 0 0 0 0 0 1 12 0 1 1 1.936593652 0
4258-1986 0 0 0 0 0 0 1 12 0 1 1 1.601009250 0
4258-1987 0 0 0 0 0 0 1 12 0 1 1 1.711333513 0
4261-1980 0 0 0 0 0 0 1 6 0 0 0 1.854151726 0
4261-1981 0 0 0 0 0 0 1 6 0 0 0 1.805129647 1
4261-1982 0 0 0 0 0 0 1 6 0 0 0 1.872824907 0
4261-1983 0 0 0 0 0 0 1 6 0 1 0 1.978112459 0
4261-1984 0 0 0 0 0 0 1 6 0 1 1 1.999407887 0
4261-1985 0 0 0 0 0 0 1 6 0 0 0 2.188746452 0
4261-1986 0 0 0 0 0 0 1 6 0 0 0 2.074398279 0
4261-1987 0 0 0 0 0 0 1 6 0 0 0 1.504884839 0
4264-1980 0 0 0 0 0 0 1 10 0 0 0 1.229391217 0
4264-1981 0 0 0 0 0 0 1 10 0 1 0 1.418340921 1
4264-1982 0 0 0 0 0 0 1 10 0 1 1 1.070392251 0
4264-1983 0 0 0 0 0 0 1 10 0 1 0 0.820724905 0
4264-1984 0 0 0 0 0 0 1 10 0 1 0 1.236495972 0
4264-1985 0 0 0 0 0 0 1 10 0 1 0 1.291503787 0
4264-1986 0 0 0 0 0 0 1 10 0 1 0 1.360231757 0
4264-1987 0 1 0 0 0 0 1 10 0 1 0 1.034670830 0
4278-1980 0 0 0 0 0 0 1 12 0 0 0 1.802247763 0
4278-1981 0 0 0 0 0 0 1 12 0 0 0 1.785328627 1
4278-1982 0 0 0 0 0 0 1 12 0 0 0 1.815666556 0
4278-1983 0 0 0 0 0 0 1 12 0 0 0 1.875983000 0
4278-1984 0 0 0 0 0 0 1 12 0 1 0 1.800329447 0
4278-1985 0 0 0 0 0 0 1 12 0 0 0 1.820029020 0
4278-1986 0 0 0 0 0 0 1 12 0 0 0 1.475531578 0
4278-1987 0 0 0 0 0 0 1 12 0 0 0 1.800216198 0
4297-1980 0 0 0 0 0 0 1 12 0 0 1 2.112708807 0
4297-1981 0 0 0 0 0 0 1 12 0 1 0 2.229253769 1
4297-1982 0 0 0 0 0 0 1 12 0 0 0 1.533609152 0
4297-1983 0 0 0 0 0 0 1 12 0 0 0 1.638398767 0
4297-1984 0 0 0 0 0 0 1 12 0 0 0 1.699027658 0
4297-1985 0 0 0 0 0 0 1 12 0 0 0 1.617568851 0
4297-1986 0 0 0 0 0 0 1 12 0 0 0 1.630912304 0
4297-1987 0 0 0 0 0 0 1 12 0 0 0 1.704527259 0
4302-1980 0 0 0 0 0 0 1 11 0 1 0 1.061952591 0
4302-1981 0 0 0 0 0 0 1 11 0 1 0 1.016822815 1
4302-1982 0 0 0 0 0 0 1 11 0 1 0 1.244216204 0
4302-1983 0 0 0 0 0 0 1 11 0 1 0 1.169463992 0
4302-1984 0 0 0 0 0 0 1 11 0 1 0 1.105809569 0
4302-1985 0 0 0 0 0 1 1 11 0 1 0 0.637577355 0
4302-1986 0 0 0 0 0 1 1 11 0 1 0 0.609541595 0
4302-1987 0 0 0 1 0 1 1 11 0 0 0 1.715748429 0
4321-1980 0 0 0 0 0 0 0 11 0 1 0 1.721292853 0
4321-1981 0 0 0 0 0 0 0 11 0 1 1 1.981609344 1
4321-1982 0 0 0 0 0 0 0 11 0 1 0 1.209655643 0
4321-1983 0 0 0 0 0 0 0 11 0 0 1 1.467286825 0
4321-1984 0 0 0 0 0 0 0 11 0 0 1 1.797547817 0
4321-1985 0 0 0 0 0 0 0 11 0 0 1 2.153104544 0
4321-1986 0 0 0 0 0 0 0 11 1 0 1 1.991016626 0
4321-1987 0 0 0 0 0 0 0 11 1 0 1 2.183852434 0
4328-1980 0 0 0 0 0 0 0 12 0 0 0 1.742112517 0
4328-1981 0 0 0 0 0 0 0 12 0 1 0 1.360412717 1
4328-1982 0 0 0 0 0 0 0 12 0 1 0 1.289857507 0
4328-1983 0 0 0 0 0 0 0 12 0 0 0 1.224947214 0
4328-1984 0 0 0 0 0 0 0 12 0 0 0 1.212542772 0
4328-1985 0 0 0 0 0 0 0 12 0 0 0 1.133723378 0
4328-1986 0 0 0 0 0 0 0 12 0 0 0 1.112820029 0
4328-1987 0 0 0 0 0 0 0 12 0 0 0 1.311340809 0
4332-1980 0 0 0 1 0 0 0 12 0 0 0 0.406412601 0
4332-1981 0 0 0 1 0 0 0 12 0 0 0 0.040821996 1
4332-1982 0 0 0 1 0 0 0 12 0 0 0 0.991140544 0
4332-1983 0 0 0 1 0 0 0 12 0 0 0 0.512553811 0
4332-1984 0 1 0 0 0 0 0 12 0 0 0 0.731779933 0
4332-1985 0 1 0 0 0 0 0 12 0 1 0 1.207639694 0
4332-1986 0 1 0 0 0 0 0 12 0 1 0 1.340429068 0
4332-1987 0 0 0 0 0 0 0 12 0 1 0 1.348405838 0
4335-1980 0 0 0 0 0 0 0 11 0 0 0 1.543309689 0
4335-1981 0 0 0 0 0 0 0 11 0 0 0 1.683545828 1
4335-1982 0 0 0 0 0 0 0 11 0 0 0 1.479456663 0
4335-1983 0 0 0 0 0 0 0 11 0 1 0 1.150045991 0
4335-1984 0 0 0 0 0 0 0 11 0 1 0 1.142201304 0
4335-1985 0 0 0 0 0 0 0 11 1 0 0 1.708803415 0
4335-1986 0 0 0 0 1 0 0 11 0 0 0 1.745894194 0
4335-1987 0 0 0 0 1 0 0 11 0 0 0 1.706928253 0
4357-1980 0 0 0 0 0 0 0 12 0 0 1 2.141146660 0
4357-1981 0 0 0 0 0 0 0 12 1 0 1 2.064174175 1
4357-1982 0 1 0 1 0 0 0 12 0 0 0 1.407255888 0
4357-1983 0 1 0 1 0 0 0 12 0 0 0 1.486518145 0
4357-1984 0 0 0 1 0 0 0 12 0 0 0 1.512647390 0
4357-1985 0 1 1 0 0 0 0 12 0 0 0 1.616430044 0
4357-1986 0 0 0 1 0 0 0 12 0 0 1 1.730626702 0
4357-1987 0 0 0 1 0 0 0 12 0 0 1 1.913384914 0
4365-1980 0 0 0 0 0 1 0 11 0 0 0 -0.035206255 0
4365-1981 0 0 0 0 0 1 0 11 0 0 0 0.283524066 1
4365-1982 0 0 1 0 0 0 1 11 0 0 0 1.263471007 0
4365-1983 0 0 0 0 0 0 1 11 0 0 0 1.548086762 0
4365-1984 0 0 0 0 0 0 1 11 0 0 0 2.068997145 0
4365-1985 0 0 0 1 0 0 1 11 0 0 0 1.490736723 0
4365-1986 0 0 0 0 0 0 1 11 0 0 0 1.775164604 0
4365-1987 0 0 0 0 0 1 0 11 1 0 0 1.125572443 0
4380-1980 0 0 0 0 0 0 0 13 0 0 1 1.810905099 0
4380-1981 0 0 0 0 0 0 0 13 0 0 1 1.951389670 1
4380-1982 0 0 0 0 0 0 0 13 0 0 1 1.977311730 0
4380-1983 0 0 0 0 0 0 0 13 0 0 1 2.114796400 0
4380-1984 0 0 0 0 0 0 0 13 0 1 1 2.197041750 0
4380-1985 0 0 0 0 0 0 0 13 0 0 0 2.198225021 0
4380-1986 0 0 0 0 0 0 0 13 0 0 0 1.938266158 0
4380-1987 0 0 0 0 0 0 0 13 0 0 0 1.960460663 0
4394-1980 0 0 0 0 0 0 0 11 0 0 0 1.630321145 0
4394-1981 0 0 0 0 0 0 0 11 0 0 1 2.089010954 1
4394-1982 0 0 0 0 0 0 0 11 0 0 0 2.015234709 0
4394-1983 0 0 0 0 0 0 0 11 0 0 1 2.034294367 0
4394-1984 0 0 0 0 0 0 0 11 0 0 0 2.088011503 0
4394-1985 0 0 0 0 0 0 0 11 0 0 0 1.797214270 0
4394-1986 0 0 0 0 0 0 1 11 0 0 0 2.321258307 0
4394-1987 0 0 0 0 0 0 0 11 0 0 0 1.524606705 0
4510-1980 0 0 0 0 0 0 0 13 0 0 0 1.304898739 0
4510-1981 0 0 0 0 0 0 0 13 0 0 1 1.630491376 1
4510-1982 0 0 0 0 0 0 0 13 0 0 0 1.651837587 0
4510-1983 0 0 0 0 0 0 0 13 0 1 0 2.255269289 0
4510-1984 0 0 0 0 0 0 0 13 0 0 0 1.905689955 0
4510-1985 0 0 0 0 0 0 0 13 0 0 0 1.703077316 0
4510-1986 0 0 0 0 0 0 0 13 0 0 0 2.028096914 0
4510-1987 0 0 0 0 1 0 0 13 0 0 0 2.340356112 0
4559-1980 0 0 0 0 0 0 0 12 0 0 0 1.323826790 0
4559-1981 0 0 0 0 0 0 0 12 0 0 0 1.450832844 1
4559-1982 0 0 0 0 0 0 0 12 0 0 0 1.297351480 0
4559-1983 0 0 0 0 0 0 0 12 0 1 0 1.393658519 0
4559-1984 0 1 0 0 0 0 0 12 1 0 0 1.005258560 0
4559-1985 0 0 0 0 0 0 0 12 0 0 0 1.491696119 0
4559-1986 0 0 0 0 0 0 0 12 0 0 0 1.568891764 0
4559-1987 0 0 0 0 0 0 0 12 0 0 0 1.599149823 0
4563-1980 1 0 0 0 0 0 0 11 0 0 1 0.890583992 0
4563-1981 0 0 0 0 0 0 0 11 0 1 0 0.927062809 1
4563-1982 0 0 0 0 0 0 0 11 0 1 0 1.101957917 0
4563-1983 0 0 0 0 0 0 0 11 0 1 0 1.047879577 0
4563-1984 0 0 0 0 0 0 0 11 0 1 0 1.760507941 0
4563-1985 0 0 0 0 0 0 0 11 0 1 0 1.310137868 0
4563-1986 0 0 0 0 0 0 0 11 0 1 0 1.667331934 0
4563-1987 0 0 0 0 0 0 0 11 0 0 1 1.711747527 0
4569-1980 0 0 0 0 0 0 0 12 0 1 1 2.267019510 0
4569-1981 0 0 0 0 0 0 0 12 0 1 1 2.125205040 1
4569-1982 0 0 0 0 0 0 0 12 0 1 1 2.073495626 0
4569-1983 0 0 0 0 0 0 0 12 0 1 1 2.043863773 0
4569-1984 0 0 0 0 0 0 0 12 0 1 1 2.367184877 0
4569-1985 0 0 0 0 0 0 0 12 0 1 1 2.129067659 0
4569-1986 0 0 0 0 0 0 0 12 0 1 1 2.033576250 0
4569-1987 0 0 0 0 0 0 0 12 0 1 1 2.035432339 0
4603-1980 0 0 0 0 0 0 0 11 0 1 1 2.055204391 0
4603-1981 0 0 0 0 0 0 0 11 0 1 1 1.997861505 1
4603-1982 0 0 0 0 0 0 0 11 0 1 1 2.038810015 0
4603-1983 0 0 0 0 0 0 0 11 0 1 1 2.174103975 0
4603-1984 0 0 0 0 0 0 0 11 0 1 1 1.988279462 0
4603-1985 0 0 0 0 0 0 0 11 0 1 1 1.921911716 0
4603-1986 0 0 0 0 0 0 0 11 0 1 1 2.035287142 0
4603-1987 0 0 0 0 0 0 0 11 0 1 1 1.853912354 0
4607-1980 0 0 0 0 0 0 0 13 0 0 0 -0.696018040 0
4607-1981 0 1 0 0 0 0 0 13 0 0 0 1.718973756 1
4607-1982 0 1 0 0 0 0 0 13 0 0 0 1.805756927 0
4607-1983 0 1 0 0 0 0 0 13 0 0 0 1.236358285 0
4607-1984 0 1 0 0 0 1 0 13 0 1 0 1.838750482 0
4607-1985 0 0 0 0 0 1 0 13 0 0 0 1.615743518 0
4607-1986 0 0 0 0 0 1 0 13 0 0 0 1.582990766 0
4607-1987 0 0 0 0 0 0 0 13 0 0 1 1.948359251 0
4633-1980 0 0 0 0 0 0 0 12 0 1 0 1.759466529 0
4633-1981 0 0 0 0 0 0 0 12 0 1 0 1.423335671 1
4633-1982 0 0 0 0 0 0 0 12 0 1 0 1.446897507 0
4633-1983 0 0 0 0 0 0 0 12 0 1 0 1.547217965 0
4633-1984 0 0 0 0 0 0 0 12 0 0 0 1.543262362 0
4633-1985 0 0 0 0 0 0 0 12 0 1 0 1.514210343 0
4633-1986 0 0 0 0 0 0 0 12 0 1 0 1.518911839 0
4633-1987 0 0 0 0 0 0 0 12 0 0 1 2.559309006 0
4676-1980 0 1 0 0 0 0 0 10 0 1 0 0.636215031 0
4676-1981 0 0 0 0 0 0 0 10 0 1 0 0.862021089 1
4676-1982 0 0 0 0 0 0 0 10 0 1 0 1.064159751 0
4676-1983 0 0 0 0 0 0 0 10 0 0 0 1.350716591 0
4676-1984 0 0 0 0 0 0 0 10 0 0 0 1.492267013 0
4676-1985 0 0 0 0 0 0 0 10 0 1 0 1.534850001 0
4676-1986 0 0 0 0 0 0 0 10 0 0 0 1.732522488 0
4676-1987 0 0 0 0 0 0 0 10 0 0 0 1.877293587 0
4701-1980 0 0 0 0 0 0 0 12 0 0 0 1.595672011 0
4701-1981 0 0 0 0 0 0 0 12 0 0 0 1.793050647 1
4701-1982 0 0 0 0 0 0 0 12 0 0 0 1.815666556 0
4701-1983 0 0 0 0 0 0 0 12 0 0 0 2.116919756 0
4701-1984 0 0 1 0 0 0 0 12 0 0 0 2.389486790 0
4701-1985 0 0 0 1 0 0 0 12 0 0 0 2.489422083 0
4701-1986 0 0 0 0 0 0 0 12 0 0 0 2.506180763 0
4701-1987 0 0 0 0 0 0 0 12 1 0 0 2.600746155 0
4716-1980 1 0 0 0 0 0 0 12 0 0 0 0.941703439 0
4716-1981 0 0 0 0 0 0 0 12 0 0 1 1.243193507 1
4716-1982 0 0 0 0 1 0 0 12 0 0 1 1.380348444 0
4716-1983 0 0 0 0 1 0 0 12 0 0 1 1.140937448 0
4716-1984 0 0 0 0 1 0 0 12 0 0 1 1.474907041 0
4716-1985 0 0 0 0 0 0 0 12 0 0 1 1.478279710 0
4716-1986 0 0 0 0 1 0 0 12 0 0 1 1.596362472 0
4716-1987 0 0 0 0 1 0 0 12 0 0 1 1.706928253 0
4720-1980 0 0 0 0 0 0 0 12 1 0 1 2.089853525 0
4720-1981 0 0 0 0 0 0 0 12 1 0 0 2.179982662 1
4720-1982 0 0 0 0 0 0 0 12 1 0 1 2.349749088 0
4720-1983 0 0 0 0 0 1 0 12 1 0 1 2.171697140 0
4720-1984 0 0 0 0 0 1 0 12 1 0 1 2.281382799 0
4720-1985 0 1 0 0 0 1 0 12 1 0 1 2.207794428 0
4720-1986 0 0 0 0 0 1 0 12 1 0 0 2.256719828 0
4720-1987 0 1 0 0 0 1 0 12 1 0 1 2.217753887 0
4759-1980 0 0 0 0 0 0 0 12 0 0 1 1.790406585 0
4759-1981 0 0 0 0 0 0 0 12 0 0 1 1.871802211 1
4759-1982 0 0 0 0 0 0 0 12 0 0 1 1.328814745 0
4759-1983 0 0 0 0 0 1 0 12 0 0 1 1.657751441 0
4759-1984 0 0 0 0 0 1 0 12 0 1 1 1.774945855 0
4759-1985 0 0 0 0 0 1 0 12 0 0 1 1.851119637 0
4759-1986 0 0 0 0 0 1 0 12 0 0 1 1.900044918 0
4759-1987 0 0 0 0 0 1 0 12 0 0 0 1.952050686 0
4791-1980 0 0 0 0 0 0 0 12 0 0 1 1.961678267 0
4791-1981 0 0 0 0 0 0 0 12 0 0 1 1.654558301 1
4791-1982 0 0 0 0 0 0 0 12 0 0 1 1.764210224 0
4791-1983 0 0 0 0 0 0 0 12 0 0 1 1.700092316 0
4791-1984 0 0 0 0 0 0 0 12 0 0 1 1.781913400 0
4791-1985 0 0 0 0 0 0 0 12 0 0 1 1.752318978 0
4791-1986 0 0 0 0 0 0 0 12 0 0 1 1.865782857 0
4791-1987 0 0 0 0 0 0 0 12 0 0 1 1.767781258 0
4811-1980 0 0 0 0 0 0 0 12 0 1 0 0.732142150 0
4811-1981 0 0 0 0 0 0 0 12 0 1 0 0.976242065 1
4811-1982 0 0 0 0 0 0 0 12 0 1 0 0.745056033 0
4811-1983 0 0 0 0 0 0 0 12 0 1 0 1.059994340 0
4811-1984 0 0 0 0 0 0 0 12 0 0 1 1.578016877 0
4811-1985 0 0 0 0 0 0 0 12 0 0 0 1.730496764 0
4811-1986 0 0 0 0 0 0 0 12 0 0 0 1.723421335 0
4811-1987 0 0 0 0 0 0 0 12 0 0 1 1.934612632 0
4828-1980 0 1 0 1 0 0 0 11 0 0 0 0.988561392 0
4828-1981 0 1 1 0 0 0 0 11 0 0 0 1.501263738 1
4828-1982 0 0 0 0 0 0 0 11 0 0 1 1.801636696 0
4828-1983 0 0 0 0 0 0 0 11 0 0 0 1.097416997 0
4828-1984 0 0 0 0 0 0 0 11 0 0 0 1.028619885 0
4828-1985 0 1 0 0 0 0 0 11 0 1 0 1.336742640 0
4828-1986 0 1 1 0 0 0 0 11 0 0 0 1.711492777 0
4828-1987 0 1 1 0 0 0 0 11 0 0 0 1.118540764 0
d82 d83 d84 d85 d86 d87 expersq
13-1980 0 0 0 0 0 0 1
13-1981 0 0 0 0 0 0 4
13-1982 1 0 0 0 0 0 9
13-1983 0 1 0 0 0 0 16
13-1984 0 0 1 0 0 0 25
13-1985 0 0 0 1 0 0 36
13-1986 0 0 0 0 1 0 49
13-1987 0 0 0 0 0 1 64
17-1980 0 0 0 0 0 0 16
17-1981 0 0 0 0 0 0 25
17-1982 1 0 0 0 0 0 36
17-1983 0 1 0 0 0 0 49
17-1984 0 0 1 0 0 0 64
17-1985 0 0 0 1 0 0 81
17-1986 0 0 0 0 1 0 100
17-1987 0 0 0 0 0 1 121
18-1980 0 0 0 0 0 0 16
18-1981 0 0 0 0 0 0 25
18-1982 1 0 0 0 0 0 36
18-1983 0 1 0 0 0 0 49
18-1984 0 0 1 0 0 0 64
18-1985 0 0 0 1 0 0 81
18-1986 0 0 0 0 1 0 100
18-1987 0 0 0 0 0 1 121
45-1980 0 0 0 0 0 0 4
45-1981 0 0 0 0 0 0 9
45-1982 1 0 0 0 0 0 16
45-1983 0 1 0 0 0 0 25
45-1984 0 0 1 0 0 0 36
45-1985 0 0 0 1 0 0 49
45-1986 0 0 0 0 1 0 64
45-1987 0 0 0 0 0 1 81
110-1980 0 0 0 0 0 0 25
110-1981 0 0 0 0 0 0 36
110-1982 1 0 0 0 0 0 49
110-1983 0 1 0 0 0 0 64
110-1984 0 0 1 0 0 0 81
110-1985 0 0 0 1 0 0 100
110-1986 0 0 0 0 1 0 121
110-1987 0 0 0 0 0 1 144
120-1980 0 0 0 0 0 0 4
120-1981 0 0 0 0 0 0 9
120-1982 1 0 0 0 0 0 16
120-1983 0 1 0 0 0 0 25
120-1984 0 0 1 0 0 0 36
120-1985 0 0 0 1 0 0 49
120-1986 0 0 0 0 1 0 64
120-1987 0 0 0 0 0 1 81
126-1980 0 0 0 0 0 0 4
126-1981 0 0 0 0 0 0 9
126-1982 1 0 0 0 0 0 16
126-1983 0 1 0 0 0 0 25
126-1984 0 0 1 0 0 0 36
126-1985 0 0 0 1 0 0 49
126-1986 0 0 0 0 1 0 64
126-1987 0 0 0 0 0 1 81
150-1980 0 0 0 0 0 0 4
150-1981 0 0 0 0 0 0 9
150-1982 1 0 0 0 0 0 16
150-1983 0 1 0 0 0 0 25
150-1984 0 0 1 0 0 0 36
150-1985 0 0 0 1 0 0 49
150-1986 0 0 0 0 1 0 64
150-1987 0 0 0 0 0 1 81
162-1980 0 0 0 0 0 0 4
162-1981 0 0 0 0 0 0 9
162-1982 1 0 0 0 0 0 16
162-1983 0 1 0 0 0 0 25
162-1984 0 0 1 0 0 0 36
162-1985 0 0 0 1 0 0 49
162-1986 0 0 0 0 1 0 64
162-1987 0 0 0 0 0 1 81
166-1980 0 0 0 0 0 0 4
166-1981 0 0 0 0 0 0 9
166-1982 1 0 0 0 0 0 16
166-1983 0 1 0 0 0 0 25
166-1984 0 0 1 0 0 0 36
166-1985 0 0 0 1 0 0 49
166-1986 0 0 0 0 1 0 64
166-1987 0 0 0 0 0 1 81
189-1980 0 0 0 0 0 0 4
189-1981 0 0 0 0 0 0 9
189-1982 1 0 0 0 0 0 16
189-1983 0 1 0 0 0 0 25
189-1984 0 0 1 0 0 0 36
189-1985 0 0 0 1 0 0 49
189-1986 0 0 0 0 1 0 64
189-1987 0 0 0 0 0 1 81
193-1980 0 0 0 0 0 0 4
193-1981 0 0 0 0 0 0 9
193-1982 1 0 0 0 0 0 16
193-1983 0 1 0 0 0 0 25
193-1984 0 0 1 0 0 0 36
193-1985 0 0 0 1 0 0 49
193-1986 0 0 0 0 1 0 64
193-1987 0 0 0 0 0 1 81
209-1980 0 0 0 0 0 0 9
209-1981 0 0 0 0 0 0 16
209-1982 1 0 0 0 0 0 25
209-1983 0 1 0 0 0 0 36
209-1984 0 0 1 0 0 0 49
209-1985 0 0 0 1 0 0 64
209-1986 0 0 0 0 1 0 81
209-1987 0 0 0 0 0 1 100
212-1980 0 0 0 0 0 0 4
212-1981 0 0 0 0 0 0 9
212-1982 1 0 0 0 0 0 16
212-1983 0 1 0 0 0 0 25
212-1984 0 0 1 0 0 0 36
212-1985 0 0 0 1 0 0 49
212-1986 0 0 0 0 1 0 64
212-1987 0 0 0 0 0 1 81
218-1980 0 0 0 0 0 0 4
218-1981 0 0 0 0 0 0 9
218-1982 1 0 0 0 0 0 16
218-1983 0 1 0 0 0 0 25
218-1984 0 0 1 0 0 0 36
218-1985 0 0 0 1 0 0 49
218-1986 0 0 0 0 1 0 64
218-1987 0 0 0 0 0 1 81
243-1980 0 0 0 0 0 0 16
243-1981 0 0 0 0 0 0 25
243-1982 1 0 0 0 0 0 36
243-1983 0 1 0 0 0 0 49
243-1984 0 0 1 0 0 0 64
243-1985 0 0 0 1 0 0 81
243-1986 0 0 0 0 1 0 100
243-1987 0 0 0 0 0 1 121
259-1980 0 0 0 0 0 0 9
259-1981 0 0 0 0 0 0 16
259-1982 1 0 0 0 0 0 25
259-1983 0 1 0 0 0 0 36
259-1984 0 0 1 0 0 0 49
259-1985 0 0 0 1 0 0 64
259-1986 0 0 0 0 1 0 81
259-1987 0 0 0 0 0 1 100
260-1980 0 0 0 0 0 0 4
260-1981 0 0 0 0 0 0 9
260-1982 1 0 0 0 0 0 16
260-1983 0 1 0 0 0 0 25
260-1984 0 0 1 0 0 0 36
260-1985 0 0 0 1 0 0 49
260-1986 0 0 0 0 1 0 64
260-1987 0 0 0 0 0 1 81
309-1980 0 0 0 0 0 0 9
309-1981 0 0 0 0 0 0 16
309-1982 1 0 0 0 0 0 25
309-1983 0 1 0 0 0 0 36
309-1984 0 0 1 0 0 0 49
309-1985 0 0 0 1 0 0 64
309-1986 0 0 0 0 1 0 81
309-1987 0 0 0 0 0 1 100
351-1980 0 0 0 0 0 0 9
351-1981 0 0 0 0 0 0 16
351-1982 1 0 0 0 0 0 25
351-1983 0 1 0 0 0 0 36
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4278-1983 0 1 0 0 0 0 36
4278-1984 0 0 1 0 0 0 49
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4278-1986 0 0 0 0 1 0 81
4278-1987 0 0 0 0 0 1 100
4297-1980 0 0 0 0 0 0 4
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4297-1984 0 0 1 0 0 0 36
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4297-1987 0 0 0 0 0 1 81
4302-1980 0 0 0 0 0 0 4
4302-1981 0 0 0 0 0 0 9
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4302-1983 0 1 0 0 0 0 25
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4302-1987 0 0 0 0 0 1 81
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4328-1983 0 1 0 0 0 0 49
4328-1984 0 0 1 0 0 0 64
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4328-1986 0 0 0 0 1 0 100
4328-1987 0 0 0 0 0 1 121
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4332-1981 0 0 0 0 0 0 9
4332-1982 1 0 0 0 0 0 16
4332-1983 0 1 0 0 0 0 25
4332-1984 0 0 1 0 0 0 36
4332-1985 0 0 0 1 0 0 49
4332-1986 0 0 0 0 1 0 64
4332-1987 0 0 0 0 0 1 81
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4335-1981 0 0 0 0 0 0 16
4335-1982 1 0 0 0 0 0 25
4335-1983 0 1 0 0 0 0 36
4335-1984 0 0 1 0 0 0 49
4335-1985 0 0 0 1 0 0 64
4335-1986 0 0 0 0 1 0 81
4335-1987 0 0 0 0 0 1 100
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4357-1983 0 1 0 0 0 0 36
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4357-1987 0 0 0 0 0 1 100
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4365-1983 0 1 0 0 0 0 25
4365-1984 0 0 1 0 0 0 36
4365-1985 0 0 0 1 0 0 49
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4365-1987 0 0 0 0 0 1 81
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4380-1982 1 0 0 0 0 0 36
4380-1983 0 1 0 0 0 0 49
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4559-1983 0 1 0 0 0 0 64
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4607-1987 0 0 0 0 0 1 81
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4633-1982 1 0 0 0 0 0 25
4633-1983 0 1 0 0 0 0 36
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4791-1987 0 0 0 0 0 1 144
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4828-1985 0 0 0 1 0 0 49
4828-1986 0 0 0 0 1 0 64
4828-1987 0 0 0 0 0 1 81
[ reached 'max' / getOption("max.print") -- omitted 2088 rows ]
Modelos Lineales con Datos Panel Estáticos Pooled OLS or POLS (Implementación en R 2)
-Estimación por OLS en :
<- lm (lwage ~ union+ + exper + I (exper^ 2 ) , data = wagepan)summary (pooled_lm_wage)
Call:
lm(formula = lwage ~ union + educ + exper + I(exper^2), data = wagepan)
Residuals:
Min 1Q Median 3Q Max
-5.3074 -0.2583 0.0369 0.2989 2.5293
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.0904635 0.0632968 -1.429 0.153
union 0.1734621 0.0171735 10.101 < 2e-16 ***
educ 0.1028767 0.0046288 22.225 < 2e-16 ***
exper 0.0992749 0.0100752 9.853 < 2e-16 ***
I(exper^2) -0.0031733 0.0007127 -4.453 8.7e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.4863 on 4355 degrees of freedom
Multiple R-squared: 0.1672, Adjusted R-squared: 0.1665
F-statistic: 218.6 on 4 and 4355 DF, p-value: < 2.2e-16
Modelos Lineales con Datos Panel Estáticos Pooled OLS or POLS (Implementación en R 2)
También podemos utilizar la función plm() con el argumento pooling lo cual tomara todo como una muestra transversal.
<- plm (lwage ~ union+ + exper + I (exper^ 2 ) , data = pdata_wage, model = "pooling" )summary (pooled_plm_wage)
Pooling Model
Call:
plm(formula = lwage ~ union + educ + exper + I(exper^2), data = pdata_wage,
model = "pooling")
Balanced Panel: n = 545, T = 8, N = 4360
Residuals:
Min. 1st Qu. Median 3rd Qu. Max.
-5.307424 -0.258340 0.036941 0.298881 2.529268
Coefficients:
Estimate Std. Error t-value Pr(>|t|)
(Intercept) -0.09046349 0.06329681 -1.4292 0.153
union 0.17346211 0.01717355 10.1005 < 2.2e-16 ***
educ 0.10287667 0.00462881 22.2253 < 2.2e-16 ***
exper 0.09927495 0.01007519 9.8534 < 2.2e-16 ***
I(exper^2) -0.00317328 0.00071269 -4.4525 8.699e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Total Sum of Squares: 1236.5
Residual Sum of Squares: 1029.7
R-Squared: 0.16723
Adj. R-Squared: 0.16647
F-statistic: 218.637 on 4 and 4355 DF, p-value: < 2.22e-16
Modelos Lineales con Datos Panel Estáticos Pooled OLS or POLS (Paréntesis)
Paréntesis: Técnicas de selección de modelos
Forward Selection (hacia adelante):
Empieza sin variables.
Va agregando la variable que más mejora el ajuste (según un criterio AIC, BIC, p-valor).
Backward Elimination (hacia atrás):
Empieza con todas las variables.
Va eliminando la menos significativa.
Stepwise (combinado):
Combina forward y backward.
Agrega y elimina variables según su contribución estadística
Modelos Lineales con Datos Panel Estáticos Pooled OLS or POLS (Paréntesis)
Funcionamiento:
Modelo inicial
Vacío, completo o parcial.
Iteración:
Incluir : probar agregar una variable que no esté.Eliminar : probar quitar una variable presente. Evaluar mejora usando:
AIC (Akaike Information Criterion) ↓
BIC (Bayesian Information Criterion) ↓
p-valores (entrada/salida)
Parar cuando no hay mejoras.
Modelos Lineales con Datos Panel Estáticos Pooled OLS or POLS (Paréntesis)
En R podemos utilizar la paquetería MASS:
p_load ('MASS' )# Ajustar modelo inicial con todas las variables <- lm (lwage ~ ., data = wagepan)# Stepwise usando AIC <- stepAIC (modelo_full, direction = "forward" )
Start: AIC=-6893.39
lwage ~ nr + year + agric + black + bus + construc + ent + exper +
fin + hisp + poorhlth + hours + manuf + married + min + nrthcen +
nrtheast + occ1 + occ2 + occ3 + occ4 + occ5 + occ6 + occ7 +
occ8 + occ9 + per + pro + pub + rur + south + educ + tra +
trad + union + d81 + d82 + d83 + d84 + d85 + d86 + d87 +
expersq
<- summary (modelo_step)$ coefficientsdim (table_sum)
Modelos Lineales con Datos Panel Estáticos Pooled OLS or POLS (Paréntesis)
Consideraciones
Riesgo de sobreajuste (overfitting): si se usan muchos predictores y pocos datos.
Ignora el contexto teórico: puede eliminar variables importantes desde el punto de vista sustantivo.
Inestabilidad: pequeños cambios en los datos pueden producir modelos distintos.
No garantiza encontrar el modelo verdadero, solo uno “óptimo” según el criterio elegido.
Modelos Lineales con Datos Panel Estáticos: POLS (Interpretación)
Recordando interpretación de coeficientes
\[Y = \beta_0 + \beta_1ln(X) + u \]
Un incremento de 1% en \(X\) está asociado con un cambio de \(\frac{\beta_1}{100}\) unidades en \(Y\)
\[ ln(Y) = \beta_0 + \beta_1X + u \]
Un cambio de una unidad en \(X\) está asociado con un incremento de \(\beta_1\) unidades en \(\ln(Y)\)
Para ser más preciso: el cambio porcentual en \(Y\) es \((e^{\beta_1} - 1) \times 100%\)
Modelos Lineales con Datos Panel Estáticos: POLS (Interpretación)
Interpretación \(\beta_1\) el cual corresponde a la variable de asociación a sindicato:
Estar afiliado a un sindicato se asocia con un incremento promedio de 18.94% unidades en la variable dependiente, manteniendo constantes las demás variables.
(Intercept)
-0.0905
Valor base del log salario cuando todo es 0.
union
0.1735
Estar en sindicato aumenta el salario ~17%.
educ
0.1029
Cada año extra de educación sube el salario ~10%.
exper
0.0993
Cada año extra de experiencia aumenta el salario ~9.9%.
I(exper^2)
-0.00317
El efecto de la experiencia disminuye con más años.
Modelos Lineales con Datos Panel Estáticos: Fixed Effects (¿Cómo funciona? )
Dado que el modelo POLS no logra controlar efectos individuales no observado que son constantes buscaremos otro métodos que lo hagan.
Efectos fijos (FE ) es un método que se enfoca en la variación dentro de cada individuo a lo largo del tiempo (within ), eliminando la variación entre individuos (between ).
Controla por individuo/agente/observación (persona, empresa, países, escuelas, hospitales, etc)
Variación within : la variación dentro de cada indiviudo a través de multiples períodos de tiempo. (Ej.: cómo cambia el salario de una persona a lo largo de los años).
Variación between : variación de una carácterística entre inviduos en un período de tiempo o en el promedio de diferentes períodos. (Ej.: comparar el salario promedio de dos personas diferentes).
Modelos Lineales con Datos Panel: Fixed Effects (¿Cómo funciona? ) Estáticos
Ejemplo de variación within
Diego
2019
160
130 +30
Diego
2020
100
130 -30
Raúl
2019
150
145 +5
Raúl
2020
140
145 -5
Modelos Lineales con Datos Panel: Fixed Effects (¿Cómo funciona? ) Estáticos
Interpretación
Variación within :
Representa cuánto difiere la observación de un individuo en un año específico respecto a su promedio personal.
Para Diego en 2019, la variación within es +30 días, es decir, 30 días más que su promedio (130 días).
En 2020, Diego tiene -30 días, es decir, 30 días menos que su promedio.
Variación between:
En este caso, la diferencia de medias entre Diego (130 días) y Raul (145 días) es de 15 días.
Modelos Lineales con Datos Panel Estáticos: Fixed Effects (¿Cómo lo implementamos? )
El método de Efectos Fijos o Efectos Within busca controlar efectos no observados constantes en el tiempo. como lo son las características individuales no medidas.
Método de transformación de efecto fijo o absorción del efecto fijo (absorbing fixed effect)
Teniendo al menos dos períodos de tiempo obtenemos el promedio de la ecuación de POLS:
\[ y_{it}= \textbf{x}_{it}\boldsymbol{\beta} + c_{i}+ u_{it} ~~~t=1,2,...T\]
Modelos Lineales con Datos Panel Estáticos: Fixed Effects (¿Cómo lo implementamos? )
Obtenemos:
\[\bar{y}_{i} = {\bar{x}_{i}}\beta + c_i + \bar{u}_{i}\]
Substrayendo la ecuación de medias de POLS:
\[ y_{it} - \bar{y}_{i} = (\textbf{x}_{it}-\mathbf{\bar{x}_{i}}) \boldsymbol{\beta} + c_{i} - c_{i}+ u_{it} - \bar{u}_{i}\]
\[ y_{it} - \bar{y}_{i} = (\textbf{x}_{it}-\mathbf{\bar{x}_{i}})\boldsymbol{\beta} + u_{it} - \bar{u}_{i}\]
Modelos Lineales con Datos Panel Estáticos: Fixed Effects (¿Cómo lo implementamos? )
Podemos representar la ecuación transformado de efectos fijos de la siguiente forma:
\[ \ddot{y}_{it} = \mathbf{\ddot{x}_{it}}\boldsymbol{\beta} + \ddot{u}_{it} ~~~t=1,2,...T \] Donde:
\[ \ddot{y}_{it} \equiv y_{it} - \bar{y}_{i}\] \[ \mathbf{\ddot{x}_{it}} \equiv \textbf{x}_{it} - \mathbf{\bar{x}_{i}}\] \[ \ddot{u}_{it} \equiv u{it} - \bar{u}_{i}\]
Modelos Lineales con Datos Panel Estáticos: Fixed Effects (¿Cómo lo implementamos? )
La transformación within elimina todo lo que es constante en el tiempo para cada individuo.
Trabaja únicamente con la variación temporal de cada individuo, lo que garantiza que la estimación de \(\beta\) de interés no esté sesgada por características no observadas y constantes en el tiempo.
En otras palabras, el estimador de efectos fijos “controla” por todo aquello que no cambia para un individuo, aunque no lo midamos explícitamente.
Modelos Lineales con Datos Panel Estáticos: Fixed Effects (Supuestos)
FE.1 Exogeneidad estricta: \[E( \ddot{u}_{it}| \mathbf{{x}_{i}} ) = E( {u}_{it}| \mathbf{{x}_{i}} ) -E( \bar{u}_{it}| \mathbf{{x}_{i}} ) = 0\] Lo cual implica que:
\[E( \ddot{u}_{it}| \mathbf{\ddot{x}_{i1}},..., \mathbf{\ddot{x}_{iT}} ) = 0\] Dado que \(\mathbf{\ddot{x}_{it}}\) es una función de:
\[ \mathbf{{x}_{i}}= ( \mathbf{{x}_{i1},... \mathbf{{x}_{iT}} } ) \]
Satisface la condición de expectativa condicional 0.
Modelos Lineales con Datos Panel Estáticos: Fixed Effects (Supuestos)
En FE se permite arbitrariamente que:
\[E( \textbf{x}_{i}'| c_{i}) \neq 0\]
Es decir, se permite que las variables omitidas estén correlacionadas con las variables observadas \(\textbf{x}_{it}\)
Dado lo anterior, no se podrá disntinguir el efecto de las \(\textbf{c}_{i}\) y de las variables constantes observables \(\textbf{x}_{t}\) , por lo tanto no se incluyen regresores constantes en el tiempo.
A nivel individual variables como el sexo o grupo étnico; a nivel empresa la industria; a nivel ciudad la distancia con un río o el clima.
Modelos Lineales con Datos Panel Estáticos: Fixed Effects (Precisión en supuestos)
Diferencia entre supuesto condicional y no condicional
Condicional \(E(\mathbf{x}_i' \mid c_i) = 0\) : supuesto de independencia estricta respecto a efectos no observados
No condicional \(E( c_i \mathbf{x}_i') =0\) :
Lectura : el valor esperado del producto \(\mathbf{x}_i'c_i\) es cero
Interpretación : Permite que \(c_i\) y \(\mathbf{x}_i\) están correlacionados dentro de ciertos grupos, siempre que esas correlaciones positivas y negativas se compensen al promediar (no hay correlación en media)
Modelos Lineales con Datos Panel Estáticos: Efectos Fijos (Fixed Effects) (Supuestos)
Condicional : independencia media dentro de cada grupo definido por Muy fuerte y útil para modelos de efectos aleatorios o independencia estricta.
No condicional :independencia media en toda la población. Más débil y no garantiza ausencia de sesgo.
Modelos Lineales con Datos Panel Estáticos: Fixed Effects (Supuestos)
FE2. No multicolinealidad (no hay dependencia lineal exacta) :
\[ rank[\sum_{t=1}^{T}E( \mathbf{\ddot{x}_{it}}' \mathbf{\ddot{x}_{it}})] = K \] - Si \(\mathbf{{x}_{it}}\) contiene alguna variable que no cambie en el tiempo para cada \(i\) , entonces \(\mathbf{\ddot{x}_{it}}\) será igual a 0 en cada período.
No permite la inclusión de variables constantes en el tiempo en su estimación como el sexo o variables geográficas.
Columna de ceros viola este supuesto, porque no hay información dentro del individuo para estimar el coeficiente.
Modelos Lineales con Datos Panel Estáticos: Fixed Effects (Supuestos)
FE3. Eficiencia del estimador FE
\[\mathbf{E}(\mathbf{u}_i \mathbf{u}_i' \mid \mathbf{x}_i, c_i) = \sigma_u^2 \mathbf{I}_T\]
Varianza constante : los errores idiosincráticos \(u_{it}\) tienen varianza constante en todos los periodos \(t\) para cada individuo \(i\) .
No autocorrelación : los errores idiosincráticos son independientes a lo largo del tiempo (no hay correlación serial).
Modelos Lineales con Datos Panel Estáticos: Fixed Effects (Supuestos)
FE.3 puede ser equivalentea RE.3 en Random Effects :
Si FE.1 se cumple \(\mathbf{E}(\mathbf{u}_i \mid \mathbf{x}_i, c_i) = 0\)
La esperanza incondicional es igual a la condicional \(\mathbf{E}(\mathbf{u}_i \mathbf{u}_i' \mid \mathbf{x}_i, c_i) =\mathbf{E}(\mathbf{u}_i \mathbf{u}_i' )\)
Tendrá la forma de \(\sigma_u^2 I_T\) .
Sin embargo, no es necesariamente el más eficiente, porque FE.1 no impone restricciones sobre la varianza-covarianza de los errores.
Modelos Lineales con Datos Panel Estáticos: Fixed Effects (Estimador)
El estimador within se representa como: \[ \hat\beta_{FE} = ( \sum_{i=1}^{N}\sum_{t=1}^{T} \mathbf{\ddot{x}_{it}}' \mathbf{\ddot{x}_{it}})^{-1} (\sum_{i=1}^{N}\sum_{t=1}^{T} \mathbf{\ddot{x}_{it}}' \ddot{y}_{it}) \]
Por FE.1 y por FE.2 (versión de muestra finita) el estimador \(\boldsymbol{\hat\beta}_{FE}\) es insesgado.
Modelos Lineales con Datos Panel Estáticos: Fixed Effects (Ejemplo)
\[ Esperanza_{it} =\beta_i + log(PIBpercap)_{it}\beta_1 + u_{it}\]
Controlar por cada individuo permitiendo que el intercepto cambie para cada \(i\)
Modelos Lineales con Datos Panel Estáticos: Fixed Effects (Ejemplo)
Tendremos un \(\beta_{Mexico}\) , \(\beta_{Argentina}\) y \(\beta_{Turkey}\)
# A tibble: 1,704 × 6
country continent year lifeExp pop gdpPercap
<fct> <fct> <int> <dbl> <int> <dbl>
1 Afghanistan Asia 1952 28.8 8425333 779.
2 Afghanistan Asia 1957 30.3 9240934 821.
3 Afghanistan Asia 1962 32.0 10267083 853.
4 Afghanistan Asia 1967 34.0 11537966 836.
5 Afghanistan Asia 1972 36.1 13079460 740.
6 Afghanistan Asia 1977 38.4 14880372 786.
7 Afghanistan Asia 1982 39.9 12881816 978.
8 Afghanistan Asia 1987 40.8 13867957 852.
9 Afghanistan Asia 1992 41.7 16317921 649.
10 Afghanistan Asia 1997 41.8 22227415 635.
# ℹ 1,694 more rows
Modelos Lineales con Datos Panel Estáticos Fixed Effects (Implementación en R)
Primero lo primero: Absorción o extracción de efecto fijo
p_load ('tidyverse' )<- causaldata:: gapminder#Substracción de media a esperanza de vida y log percapita <- df_gapmind |> mutate (log_PIBper = log (gdpPercap)) |> group_by (country) |> mutate (#media esperanza de vida life_exp_aver = mean (lifeExp),#Esperanza de vida within lifeExp_within = lifeExp - mean (lifeExp),#media log(pib_percapita) log_PIBper_mean = mean (log_PIBper) , #PIB within log_PIBper_within = log_PIBper - mean (log_PIBper )) |> ungroup () |> arrange (country)head (df_gapmind)
# A tibble: 6 × 11
country continent year lifeExp pop gdpPercap log_PIBper life_exp_aver
<fct> <fct> <int> <dbl> <int> <dbl> <dbl> <dbl>
1 Afghanistan Asia 1952 28.8 8.43e6 779. 6.66 37.5
2 Afghanistan Asia 1957 30.3 9.24e6 821. 6.71 37.5
3 Afghanistan Asia 1962 32.0 1.03e7 853. 6.75 37.5
4 Afghanistan Asia 1967 34.0 1.15e7 836. 6.73 37.5
5 Afghanistan Asia 1972 36.1 1.31e7 740. 6.61 37.5
6 Afghanistan Asia 1977 38.4 1.49e7 786. 6.67 37.5
# ℹ 3 more variables: lifeExp_within <dbl>, log_PIBper_mean <dbl>,
# log_PIBper_within <dbl>
Modelos Lineales con Datos Panel Estáticos Fixed Effects (Implementación en R)
Estimamos modelo de efectos fijos transformados por OLS
<- lm (lifeExp_within ~ log_PIBper_within, data = df_gapmind)summary (m_FE1)
Call:
lm(formula = lifeExp_within ~ log_PIBper_within, data = df_gapmind)
Residuals:
Min 1Q Median 3Q Max
-19.6545 -2.6950 0.0131 2.9139 16.2962
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -4.453e-17 1.227e-01 0.0 1
log_PIBper_within 9.769e+00 2.840e-01 34.4 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 5.063 on 1702 degrees of freedom
Multiple R-squared: 0.4101, Adjusted R-squared: 0.4098
F-statistic: 1183 on 1 and 1702 DF, p-value: < 2.2e-16
Modelos Lineales con Datos Panel Estáticos: Fixed Effects (Implementación en R)
Estimamos modelo de FE con función plm
p_load ('wooldridge' , 'causaldata' , 'plm' )#Convertimos a panel df <- pdata.frame (df_gapmind , index = c ("country" , "year" ))#Modelo FE con plm <- plm (lifeExp ~ log_PIBper , data = df_pdata , model = "within" , effect = 'individual' )summary (m_FE2)
Oneway (individual) effect Within Model
Call:
plm(formula = lifeExp ~ log_PIBper, data = df_pdata, effect = "individual",
model = "within")
Balanced Panel: n = 142, T = 12, N = 1704
Residuals:
Min. 1st Qu. Median 3rd Qu. Max.
-19.654463 -2.694991 0.013099 2.913864 16.296193
Coefficients:
Estimate Std. Error t-value Pr(>|t|)
log_PIBper 9.76896 0.29653 32.944 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Total Sum of Squares: 73973
Residual Sum of Squares: 43635
R-Squared: 0.41012
Adj. R-Squared: 0.35646
F-statistic: 1085.29 on 1 and 1561 DF, p-value: < 2.22e-16
Modelos Lineales con Datos Panel Estáticos: Fixed Effects (con Dummy)
Otra forma de implementarlo: Dummy por cada país
\[{y_{it} = \alpha + \beta x_{it} + \gamma_1 D_{USA} + \gamma_2 D_{Mexico} + \dots + u_{it}}\]
Captura todos los efectos fijos constantes del país.
Requiere una categoría base para evitar colinealidad.
Desventaja : si hay muchas observaciones, el número de dummies crece demasiado y el modelo pesado y poco eficiente.
Transformation within : Más eficiente con muchos individuos/países, evita problemas de colinealidad, y se centra en la variación within , que es la que nos interesa para estimar \(\beta\) .
Modelos Lineales con Datos Panel Estáticos:Fixed Effects (con Dummy en R)
En R utilizamos la función factor() para incluir cad país como dummy:
<- lm (lifeExp ~ factor (country) + log_PIBper, data = df_gapmind)summary (m_FE3)
Call:
lm(formula = lifeExp ~ factor(country) + log_PIBper, data = df_gapmind)
Residuals:
Min 1Q Median 3Q Max
-19.6545 -2.6950 0.0131 2.9139 16.2962
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -27.7735 2.5005 -11.107 < 2e-16
factor(country)Albania 17.7826 2.1952 8.101 1.09e-15
factor(country)Algeria 5.2411 2.2145 2.367 0.018069
factor(country)Angola -13.9071 2.2017 -6.316 3.48e-10
factor(country)Argentina 8.1322 2.2728 3.578 0.000357
factor(country)Australia 6.4003 2.3520 2.721 0.006577
factor(country)Austria 5.1559 2.3482 2.196 0.028264
factor(country)Bahrain -1.9682 2.3438 -0.840 0.401179
factor(country)Bangladesh 12.4011 2.1584 5.745 1.10e-08
factor(country)Belgium 5.6169 2.3492 2.391 0.016920
factor(country)Benin 7.7450 2.1611 3.584 0.000349
factor(country)Bolivia 2.3380 2.1925 1.066 0.286434
factor(country)Bosnia and Herzegovina 17.3528 2.1935 7.911 4.80e-15
factor(country)Botswana 3.1522 2.1997 1.433 0.152050
factor(country)Brazil 6.3181 2.2299 2.833 0.004665
factor(country)Bulgaria 12.6702 2.2389 5.659 1.81e-08
factor(country)Burkina Faso 6.8580 2.1585 3.177 0.001516
factor(country)Burundi 12.6464 2.1644 5.843 6.24e-09
factor(country)Cambodia 12.9167 2.1598 5.981 2.75e-09
factor(country)Cameroon 3.0620 2.1707 1.411 0.158559
factor(country)Canada 5.4647 2.3664 2.309 0.021059
factor(country)Central African Republic 4.7576 2.1590 2.204 0.027698
factor(country)Chad 5.7370 2.1611 2.655 0.008020
factor(country)Chile 9.9150 2.2425 4.421 1.05e-05
factor(country)China 21.2712 2.1604 9.846 < 2e-16
factor(country)Colombia 10.9197 2.2091 4.943 8.52e-07
factor(country)Comoros 10.2055 2.1631 4.718 2.60e-06
factor(country)Congo, Dem. Rep. 10.0249 2.1603 4.640 3.77e-06
factor(country)Congo, Rep. 1.3751 2.1978 0.626 0.531627
factor(country)Costa Rica 14.5522 2.2276 6.533 8.73e-11
factor(country)Cote d'Ivoire 2.5978 2.1733 1.195 0.232140
factor(country)Croatia 9.4630 2.2696 4.169 3.22e-05
factor(country)Cuba 13.5129 2.2426 6.025 2.10e-09
factor(country)Czech Republic 6.5554 2.3140 2.833 0.004671
factor(country)Denmark 5.3450 2.3613 2.264 0.023738
factor(country)Djibouti -2.8341 2.1876 -1.296 0.195336
factor(country)Dominican Republic 12.5829 2.1865 5.755 1.04e-08
factor(country)Ecuador 6.3606 2.2340 2.847 0.004469
factor(country)Egypt 6.5774 2.1899 3.003 0.002712
factor(country)El Salvador 5.5348 2.2166 2.497 0.012628
factor(country)Equatorial Guinea 1.0619 2.1626 0.491 0.623481
factor(country)Eritrea 12.7109 2.1622 5.879 5.05e-09
factor(country)Ethiopia 11.5290 2.1628 5.331 1.12e-07
factor(country)Finland 6.4773 2.3315 2.778 0.005531
factor(country)France 6.9102 2.3422 2.950 0.003222
factor(country)Gabon -11.4293 2.2897 -4.992 6.66e-07
factor(country)Gambia 8.5989 2.1590 3.983 7.13e-05
factor(country)Germany 5.0641 2.3535 2.152 0.031569
factor(country)Ghana 12.2924 2.1599 5.691 1.50e-08
factor(country)Greece 9.8322 2.3026 4.270 2.07e-05
factor(country)Guatemala 3.7542 2.2091 1.699 0.089435
factor(country)Guinea 6.1635 2.1585 2.855 0.004354
factor(country)Guinea-Bissau 4.0586 2.1596 1.879 0.060383
factor(country)Haiti 5.8666 2.1683 2.706 0.006893
factor(country)Honduras 8.1544 2.1904 3.723 0.000204
factor(country)Hong Kong, China 9.6640 2.3019 4.198 2.84e-05
factor(country)Hungary 6.9008 2.2881 3.016 0.002603
factor(country)Iceland 8.3929 2.3503 3.571 0.000366
factor(country)India 13.9706 2.1591 6.471 1.30e-10
factor(country)Indonesia 10.6745 2.1666 4.927 9.24e-07
factor(country)Iran 0.2559 2.2498 0.114 0.909452
factor(country)Iraq -1.8960 2.2506 -0.842 0.399678
factor(country)Ireland 8.5358 2.3088 3.697 0.000226
factor(country)Israel 9.3947 2.3064 4.073 4.87e-05
factor(country)Italy 8.4601 2.3206 3.646 0.000275
factor(country)Jamaica 11.5001 2.2403 5.133 3.21e-07
factor(country)Japan 9.2015 2.3214 3.964 7.71e-05
factor(country)Jordan 9.4722 2.1933 4.319 1.67e-05
factor(country)Kenya 11.3351 2.1616 5.244 1.79e-07
factor(country)Korea, Dem. Rep. 15.6495 2.1818 7.173 1.13e-12
factor(country)Korea, Rep. 9.4547 2.2270 4.245 2.31e-05
factor(country)Kuwait -10.3442 2.5036 -4.132 3.79e-05
factor(country)Lebanon 7.0391 2.2536 3.123 0.001820
factor(country)Lesotho 13.9758 2.1589 6.474 1.28e-10
factor(country)Liberia 7.8041 2.1601 3.613 0.000312
factor(country)Libya -2.9242 2.2854 -1.279 0.200913
factor(country)Madagascar 5.4748 2.1634 2.531 0.011483
factor(country)Malawi 9.2660 2.1609 4.288 1.91e-05
factor(country)Malaysia 10.3093 2.2157 4.653 3.55e-06
factor(country)Mali 7.8890 2.1593 3.654 0.000267
factor(country)Mauritania 9.9067 2.1636 4.579 5.05e-06
factor(country)Mauritius 11.6102 2.2115 5.250 1.73e-07
factor(country)Mexico 6.4046 2.2552 2.840 0.004571
factor(country)Mongolia 11.7578 2.1679 5.424 6.76e-08
factor(country)Montenegro 12.1100 2.2481 5.387 8.27e-08
factor(country)Morocco 9.5733 2.1821 4.387 1.23e-05
factor(country)Mozambique 6.8808 2.1618 3.183 0.001487
factor(country)Myanmar 22.1428 2.1669 10.219 < 2e-16
factor(country)Namibia 1.2264 2.2046 0.556 0.578096
factor(country)Nepal 11.9117 2.1585 5.519 4.00e-08
factor(country)Netherlands 6.6905 2.3605 2.834 0.004651
factor(country)New Zealand 6.7521 2.3398 2.886 0.003959
factor(country)Nicaragua 7.0148 2.1990 3.190 0.001451
factor(country)Niger 7.4817 2.1585 3.466 0.000542
factor(country)Nigeria 0.2362 2.1658 0.109 0.913182
factor(country)Norway 5.2662 2.3808 2.212 0.027116
factor(country)Oman -2.6950 2.2748 -1.185 0.236298
factor(country)Pakistan 12.5242 2.1635 5.789 8.55e-09
factor(country)Panama 11.7063 2.2312 5.247 1.76e-07
factor(country)Paraguay 16.0615 2.1957 7.315 4.10e-13
factor(country)Peru 2.4684 2.2335 1.105 0.269261
factor(country)Philippines 13.9677 2.1777 6.414 1.87e-10
factor(country)Poland 10.3117 2.2629 4.557 5.60e-06
factor(country)Portugal 8.6700 2.2807 3.801 0.000149
factor(country)Puerto Rico 11.2107 2.2786 4.920 9.56e-07
factor(country)Reunion 11.9001 2.2212 5.358 9.69e-08
factor(country)Romania 9.7631 2.2510 4.337 1.54e-05
factor(country)Rwanda 5.8015 2.1591 2.687 0.007287
factor(country)Sao Tome and Principe 15.2824 2.1641 7.062 2.46e-12
factor(country)Saudi Arabia -9.3738 2.3495 -3.990 6.92e-05
factor(country)Senegal 6.7647 2.1671 3.122 0.001832
factor(country)Serbia 7.8708 2.2704 3.467 0.000541
factor(country)Sierra Leone -3.2832 2.1599 -1.520 0.128685
factor(country)Singapore 7.7617 2.2980 3.378 0.000749
factor(country)Slovak Republic 8.6514 2.2836 3.788 0.000157
factor(country)Slovenia 7.2443 2.3075 3.139 0.001724
factor(country)Somalia 0.1222 2.1609 0.057 0.954926
factor(country)South Africa -4.9006 2.2542 -2.174 0.029857
factor(country)Spain 10.4524 2.3011 4.542 5.99e-06
factor(country)Sri Lanka 21.7701 2.1697 10.034 < 2e-16
factor(country)Sudan 2.8876 2.1722 1.329 0.183920
factor(country)Swaziland -1.1013 2.1922 -0.502 0.615473
factor(country)Sweden 7.9883 2.3511 3.398 0.000697
factor(country)Switzerland 3.9627 2.3941 1.655 0.098084
factor(country)Syria 11.3248 2.1918 5.167 2.69e-07
factor(country)Taiwan 12.7718 2.2429 5.694 1.48e-08
factor(country)Tanzania 9.8807 2.1585 4.578 5.08e-06
factor(country)Thailand 14.4358 2.1809 6.619 4.95e-11
factor(country)Togo 10.6459 2.1609 4.927 9.25e-07
factor(country)Trinidad and Tobago 7.9716 2.2539 3.537 0.000417
factor(country)Tunisia 10.1077 2.1950 4.605 4.46e-06
factor(country)Turkey 6.3521 2.2115 2.872 0.004130
factor(country)Uganda 10.0855 2.1584 4.673 3.23e-06
factor(country)United Kingdom 5.9090 2.3490 2.516 0.011986
factor(country)United States 2.4768 2.3863 1.038 0.299453
factor(country)Uruguay 12.1379 2.2520 5.390 8.14e-08
factor(country)Venezuela 4.3883 2.2851 1.920 0.054991
factor(country)Vietnam 18.6392 2.1588 8.634 < 2e-16
factor(country)West Bank and Gaza 8.6575 2.2010 3.933 8.74e-05
factor(country)Yemen, Rep. 3.4847 2.1657 1.609 0.107806
factor(country)Zambia 3.4400 2.1639 1.590 0.112107
factor(country)Zimbabwe 17.5924 2.1597 8.146 7.64e-16
log_PIBper 9.7690 0.2965 32.944 < 2e-16
(Intercept) ***
factor(country)Albania ***
factor(country)Algeria *
factor(country)Angola ***
factor(country)Argentina ***
factor(country)Australia **
factor(country)Austria *
factor(country)Bahrain
factor(country)Bangladesh ***
factor(country)Belgium *
factor(country)Benin ***
factor(country)Bolivia
factor(country)Bosnia and Herzegovina ***
factor(country)Botswana
factor(country)Brazil **
factor(country)Bulgaria ***
factor(country)Burkina Faso **
factor(country)Burundi ***
factor(country)Cambodia ***
factor(country)Cameroon
factor(country)Canada *
factor(country)Central African Republic *
factor(country)Chad **
factor(country)Chile ***
factor(country)China ***
factor(country)Colombia ***
factor(country)Comoros ***
factor(country)Congo, Dem. Rep. ***
factor(country)Congo, Rep.
factor(country)Costa Rica ***
factor(country)Cote d'Ivoire
factor(country)Croatia ***
factor(country)Cuba ***
factor(country)Czech Republic **
factor(country)Denmark *
factor(country)Djibouti
factor(country)Dominican Republic ***
factor(country)Ecuador **
factor(country)Egypt **
factor(country)El Salvador *
factor(country)Equatorial Guinea
factor(country)Eritrea ***
factor(country)Ethiopia ***
factor(country)Finland **
factor(country)France **
factor(country)Gabon ***
factor(country)Gambia ***
factor(country)Germany *
factor(country)Ghana ***
factor(country)Greece ***
factor(country)Guatemala .
factor(country)Guinea **
factor(country)Guinea-Bissau .
factor(country)Haiti **
factor(country)Honduras ***
factor(country)Hong Kong, China ***
factor(country)Hungary **
factor(country)Iceland ***
factor(country)India ***
factor(country)Indonesia ***
factor(country)Iran
factor(country)Iraq
factor(country)Ireland ***
factor(country)Israel ***
factor(country)Italy ***
factor(country)Jamaica ***
factor(country)Japan ***
factor(country)Jordan ***
factor(country)Kenya ***
factor(country)Korea, Dem. Rep. ***
factor(country)Korea, Rep. ***
factor(country)Kuwait ***
factor(country)Lebanon **
factor(country)Lesotho ***
factor(country)Liberia ***
factor(country)Libya
factor(country)Madagascar *
factor(country)Malawi ***
factor(country)Malaysia ***
factor(country)Mali ***
factor(country)Mauritania ***
factor(country)Mauritius ***
factor(country)Mexico **
factor(country)Mongolia ***
factor(country)Montenegro ***
factor(country)Morocco ***
factor(country)Mozambique **
factor(country)Myanmar ***
factor(country)Namibia
factor(country)Nepal ***
factor(country)Netherlands **
factor(country)New Zealand **
factor(country)Nicaragua **
factor(country)Niger ***
factor(country)Nigeria
factor(country)Norway *
factor(country)Oman
factor(country)Pakistan ***
factor(country)Panama ***
factor(country)Paraguay ***
factor(country)Peru
factor(country)Philippines ***
factor(country)Poland ***
factor(country)Portugal ***
factor(country)Puerto Rico ***
factor(country)Reunion ***
factor(country)Romania ***
factor(country)Rwanda **
factor(country)Sao Tome and Principe ***
factor(country)Saudi Arabia ***
factor(country)Senegal **
factor(country)Serbia ***
factor(country)Sierra Leone
factor(country)Singapore ***
factor(country)Slovak Republic ***
factor(country)Slovenia **
factor(country)Somalia
factor(country)South Africa *
factor(country)Spain ***
factor(country)Sri Lanka ***
factor(country)Sudan
factor(country)Swaziland
factor(country)Sweden ***
factor(country)Switzerland .
factor(country)Syria ***
factor(country)Taiwan ***
factor(country)Tanzania ***
factor(country)Thailand ***
factor(country)Togo ***
factor(country)Trinidad and Tobago ***
factor(country)Tunisia ***
factor(country)Turkey **
factor(country)Uganda ***
factor(country)United Kingdom *
factor(country)United States
factor(country)Uruguay ***
factor(country)Venezuela .
factor(country)Vietnam ***
factor(country)West Bank and Gaza ***
factor(country)Yemen, Rep.
factor(country)Zambia
factor(country)Zimbabwe ***
log_PIBper ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 5.287 on 1561 degrees of freedom
Multiple R-squared: 0.8464, Adjusted R-squared: 0.8325
F-statistic: 60.59 on 142 and 1561 DF, p-value: < 2.2e-16
Modelos Lineales con Datos Panel Estáticos: Fixed Effect (Interpretación)
Vemos que el coeficiente del logarítmo del PIB per capita es FE: 9.769 y en POLS: 8.40
Interpretación: El coeficiente del log(gdpPercap) indica que un aumento del 1% en el PIB per cápita está asociado con un aumento de 0.09769 años (alrededor de 35.6 días) en la esperanza de vida.
Si el intercepto de México es 6.40 y el de Brasil es 6.3181, podemos decir que si México y Brasil tuvieran el mismo PIB per capita, la esperanza de vida en México podría ser 0.09 más alta.
Consideración importante: “Tener en cuenta que los efectos fijos son una buena forma de controlar una larga lista de variables no observadas constantes en el tiempo para observar el efecto de una o unas pocas variables” - Nick Huntington-Klein
Modelos Lineales con Datos Panel Estáticos: Fixed Effects (R-squared within)
R-squared within
Mide cuánto de la variación dentro de cada individuo \(i\) a lo largo del tiempo es explicado por el modelo.
Aquí estamos quitando la variación entre individuos, centrándonos solo en cambios internos.
\[
R^2_{\text{within}} = 1 - \frac{RSS_i}{TSS_i}
= 1 - \frac{\sum_{it} (y_{it} - \hat{y}_{it})^2}{\sum_{it} (y_{it} - \bar{y}_i)^2}
\]
Interpretación : “¿Cuánto cambian los valores dentro de cada unidad y es explicado por X?”
Modelos Lineales con Datos Panel Estáticos: Fixed Effects (Prueba F)
#### R-sq Within ---- <- df_gapmind |> mutate (residuos = residuals (m_FE2) ,life_exp_fit = fitted (m_FE2))# r2 = 1 - (rss/tss) <- 1 - sum (df_gapmind$ residuos^ 2 ) / sum (df_gapmind$ lifeExp_within^ 2 ) print (r.squared (m_FE2))
Modelos Lineales con Datos Panel Estáticos: Fixed Effects (Prueba F)
Prueba F: Pooled vs FE
Evalúa si existen diferencias significativas entre las unidades en sus niveles constantes a lo largo del tiempo.
En términos estadísticos la prueba F, está probando si los efectos individuales (interceptos) son todos iguales en cada \(i\) o si al menos uno es distinto.
Hipótesis
\(H_0\) : \(\beta_{i} = 0\) → No hay diferencias individuales (Pooled OLS adecuado).\(H_1\) : \(\beta_{i} \neq 0\) → Hay al menos un efecto fijo (FE adecuado).
Interpretación : si se rechaza \(H_0\) (p-valor < 0.05), existe al menos un efecto no observado individual significativo. Por lo tanto el modelo de FE es adecuado.
Modelos Lineales con Datos Panel Estáticos: Fixed Effects (Prueba F)
Utilizamos la función pFtest() de la paquetería plm
Sintáxis : pFtest(modelo FE, modelo pooled,)
#Datos <- pdata.frame (gapminder, index = c ("country" , "year" ))#Pooled <- plm (lifeExp ~ log (gdpPercap) , data = df_paneld, model = 'pooling' )#FE <- plm (lifeExp ~ log_PIBper , data = df_pdata , model = "within" , effect = 'individual' )# Test F para efectos individuales (Pooled vs EF) <- pFtest (m_FE2,pooled_plm)print (f_test)
F test for individual effects
data: lifeExp ~ log_PIBper
F = 14, df1 = 141, df2 = 1561, p-value < 2.2e-16
alternative hypothesis: significant effects
Modelos Lineales con Datos Panel Estáticos :Fixed Effects (Ejemplo 2)
Continuamos con la función de salarios la cual será estimada por el método de FE:
\[ log(wage)_{it} =\beta_i + union_{it}\beta_1 + educ_{it}\beta_2 + exp_{it}\beta_3 + exp^2_{it}\beta_4 + u_{it} \]
Modelos Lineales con Datos Panel Estáticos :Fixed Effects (Ejemplo 2)
library (pacman)p_load ('wooldridge' , 'plm' , "modelsummary" )data ("wagepan" )#Data <- pdata.frame (wagepan, index = c ("nr" , "year" ))#Pooled <- plm (lwage ~ union + educ + exper + I (exper^ 2 ) , data = pdata_wage, model = 'pooling' )#Efectos Fijos <- plm (lwage ~ union + educ + exper + I (exper^ 2 ) , data = pdata_wage, model = "within" , effect = 'individual' )summary (FE_plm_wage)
Oneway (individual) effect Within Model
Call:
plm(formula = lwage ~ union + educ + exper + I(exper^2), data = pdata_wage,
effect = "individual", model = "within")
Balanced Panel: n = 545, T = 8, N = 4360
Residuals:
Min. 1st Qu. Median 3rd Qu. Max.
-4.175074 -0.124834 0.008003 0.158338 1.487799
Coefficients:
Estimate Std. Error t-value Pr(>|t|)
union 0.08333385 0.01929709 4.3185 1.611e-05 ***
exper 0.12193311 0.00817035 14.9238 < 2.2e-16 ***
I(exper^2) -0.00448202 0.00060123 -7.4547 1.109e-13 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Total Sum of Squares: 572.05
Residual Sum of Squares: 470.96
R-Squared: 0.17672
Adj. R-Squared: 0.058588
F-statistic: 272.76 on 3 and 3812 DF, p-value: < 2.22e-16
Modelos Lineales con Datos Panel Estáticos :Fixed Effects (Ejemplo 2: Prueba F)
Comparamos POLS y FE mediante prueba F:
#F-test <- pFtest (FE_plm_wage,pooled_plm_wage)print (f_test_wage)
F test for individual effects
data: lwage ~ union + educ + exper + I(exper^2)
F = 8.3294, df1 = 543, df2 = 3812, p-value < 2.2e-16
alternative hypothesis: significant effects
Modelos Lineales con Datos Panel Estáticos: Efectos fijos de dos vías (Two-Way Fixed Effects)
Efectos fijos de dos vías (Two-Way Fixed Effects)
No sólo tendremos un intercepto que cambié por cada individuo \(\beta_{i}\) , también tendremos un intercepto que cambie por cada período \(\beta_{t}\) :
\[y_{it} =\beta_i + \beta_t + x_{it}\gamma_i + u_{it} \]
Con los FE por \(i\) , tratamos de eliminar la variación entre unidades (países, individuos, etc.) y nos centramos en la variación dentro de la unidad a lo largo del tiempo.
Con los FE por cada \(t\) , tratamos de controlar la variación a lo largo del tiempo y nos centramos en la variación entre unidades dentro de un mismo período. (Shocks económicos)
Modelos Lineales con Datos Panel Estáticos: Two-Way Fixed Effects (Double Demeaning)
Utilizando la transformación within o double demeaning :
\[\ddot{Y}_{it} = Y_{it} - \bar{Y}_{i} - \bar{Y}_{ t} + \bar{Y}_{\cdot\cdot}\]
Donde:\(\bar{Y}_{i}\) = promedio de la unidad \(i\) (en todos los \(t\) )\(\bar{Y}_{t}\) = promedio del período \(t\) (en todas las unidades)\(\bar{Y}_{\cdot\cdot}\) = promedio global
Modelos Lineales con Datos Panel Estáticos: Two-Way Fixed Effects (Double Demeaning)
1️⃣ Restar promedio por unidad → elimina diferencias entre unidades .Restar promedio por tiempo → elimina diferencias entre períodos .Sumar promedio global → corrige doble resta.
Ejemplo:
Diego
2019
160
130 +30
Diego
2020
100
130 -30
Raúl
2019
150
145 +5
Raúl
2020
140
145 -5
Modelos Lineales con Datos Panel Estáticos: Two-Way Fixed Effects (Double Demeaning)
Media por año (efecto tiempo)
Media total
Modelos Lineales con Datos Panel Estáticos: Two-Way Fixed Effects (Double Demeaning)
Con las medias por año y global podemos calcular la transformación Double Demeaning:
\(\ddot{h}_{it} = h_{it} - \bar{h}_{i} - \bar{h}_{t} + \bar{h}_{\cdot\cdot}\)
Diego
2019
160 - 130 - 155 + 137.5
+12.5
Diego
2020
100 - 130 - 120 + 137.5
-12.5
Raúl
2019
150 - 145 - 155 + 137.5
-12.5
Raúl
2020
140 - 145 - 120 + 137.5
+12.5
Valores positivos: más que la combinación de media persona y media año
Valores negativos: menos que la combinación de media persona y media año
Modelos Lineales con Datos Panel Estáticos: Two-Way Fixed Effects (Double demeaning en R)
Para la transformación double demeaning (sustracción de medias por dos dimensiones) retomamos el ejemplo de la esperanza de vida y pib por método within (sustracción de la media por país):
p_load ('tidyverse' )<- causaldata:: gapminder#Substracción de media a esperanza de vida y log percapita <- df_gapmind |> mutate (log_PIBper = log (gdpPercap)) |> group_by (country) |> mutate (#media esperanza de vida life_exp_aver = mean (lifeExp),#Esperanza de vida within lifeExp_within = lifeExp - mean (lifeExp),#media log(pib_percapita) log_PIBper_mean = mean (log_PIBper) , #PIB within log_PIBper_within = log_PIBper - mean (log_PIBper )) |> ungroup () |> arrange (country)head (df_gapmind)
# A tibble: 6 × 11
country continent year lifeExp pop gdpPercap log_PIBper life_exp_aver
<fct> <fct> <int> <dbl> <int> <dbl> <dbl> <dbl>
1 Afghanistan Asia 1952 28.8 8.43e6 779. 6.66 37.5
2 Afghanistan Asia 1957 30.3 9.24e6 821. 6.71 37.5
3 Afghanistan Asia 1962 32.0 1.03e7 853. 6.75 37.5
4 Afghanistan Asia 1967 34.0 1.15e7 836. 6.73 37.5
5 Afghanistan Asia 1972 36.1 1.31e7 740. 6.61 37.5
6 Afghanistan Asia 1977 38.4 1.49e7 786. 6.67 37.5
# ℹ 3 more variables: lifeExp_within <dbl>, log_PIBper_mean <dbl>,
# log_PIBper_within <dbl>
Modelos Lineales con Datos Panel Estáticos: Two-Way Fixed Effects (Double demeaning en R)
¿Qué nos falta para realizar un TWFE con transfromación Double Demeaning?
Calculamos la medias por año y totales tanto de la \(Esperanza_i\) así como del \(log(PIBpercap)\) :
## Substracción de media doble (Doubledemeaning ) ---- #Media por año y media global <- df_gapmind |> group_by (year) |> mutate (lifeExp_year_mean = mean (lifeExp),logPIBper_year_mean = mean (log_PIBper)) |> ungroup () |> mutate (lifeExp_global_mean = mean (lifeExp),logPIBper_global_mean = mean (log_PIBper))
Modelos Lineales con Datos Panel Estáticos: Two-Way Fixed Effects (Double demeaning en R)
Con esto podemos calcular las variables transformadas:
#Creación de variables Double Demeaning yit−yˉi⋅−yˉ⋅t+yˉ⋅⋅ <- df_gapmind |> mutate ( lifeExp_within_2way = lifeExp - life_exp_aver - lifeExp_year_mean + lifeExp_global_mean,logPIBper_within_2way = log_PIBper - log_PIBper_mean - logPIBper_year_mean + logPIBper_global_meanhead (df_gapmind)
# A tibble: 6 × 17
country continent year lifeExp pop gdpPercap log_PIBper life_exp_aver
<fct> <fct> <int> <dbl> <int> <dbl> <dbl> <dbl>
1 Afghanistan Asia 1952 28.8 8.43e6 779. 6.66 37.5
2 Afghanistan Asia 1957 30.3 9.24e6 821. 6.71 37.5
3 Afghanistan Asia 1962 32.0 1.03e7 853. 6.75 37.5
4 Afghanistan Asia 1967 34.0 1.15e7 836. 6.73 37.5
5 Afghanistan Asia 1972 36.1 1.31e7 740. 6.61 37.5
6 Afghanistan Asia 1977 38.4 1.49e7 786. 6.67 37.5
# ℹ 9 more variables: lifeExp_within <dbl>, log_PIBper_mean <dbl>,
# log_PIBper_within <dbl>, lifeExp_year_mean <dbl>,
# logPIBper_year_mean <dbl>, lifeExp_global_mean <dbl>,
# logPIBper_global_mean <dbl>, lifeExp_within_2way <dbl>,
# logPIBper_within_2way <dbl>
Modelos Lineales con Datos Panel Estáticos: Two-Way Fixed Effects (Double demeaning en R)
Estimación de modelo Double Demeaning por OLS:
## Estimación por TWFE por transformación Doubledemeneaning ------ <- lm (lifeExp_within_2way ~ logPIBper_within_2way, data = df_gapmind)summary (m_FE2way_double)
Call:
lm(formula = lifeExp_within_2way ~ logPIBper_within_2way, data = df_gapmind)
Residuals:
Min 1Q Median 3Q Max
-22.5109 -1.8818 0.0121 1.9573 9.0051
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -3.465e-16 7.918e-02 0.000 1
logPIBper_within_2way 1.450e+00 2.553e-01 5.678 1.59e-08 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 3.269 on 1702 degrees of freedom
Multiple R-squared: 0.01859, Adjusted R-squared: 0.01802
F-statistic: 32.25 on 1 and 1702 DF, p-value: 1.595e-08
Modelos Lineales con Datos Panel Estáticos: Two-Way Fixed Effects (Implementación en R)
Estimamos el modelo de Two-Way Fixed Effects de la esperanza de vida con la función plm()
\[ Esperanza_{it} =\beta_i + \beta_t + log(PIBpercap)_{it}\beta_1 + u_{it} \]
#Convertimos a panel df <- pdata.frame (df_gapmind , index = c ("country" , "year" ))#Two-way FE <- plm (lifeExp ~ log_PIBper, data = df_pdata, model = "within" , effect = "twoways" )summary (m_twfe)
Twoways effects Within Model
Call:
plm(formula = lifeExp ~ log_PIBper, data = df_pdata, effect = "twoways",
model = "within")
Balanced Panel: n = 142, T = 12, N = 1704
Residuals:
Min. 1st Qu. Median 3rd Qu. Max.
-22.510864 -1.881758 0.012059 1.957336 9.005137
Coefficients:
Estimate Std. Error t-value Pr(>|t|)
log_PIBper 1.44986 0.26755 5.419 6.94e-08 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Total Sum of Squares: 18529
Residual Sum of Squares: 18185
R-Squared: 0.018593
Adj. R-Squared: -0.078281
F-statistic: 29.3656 on 1 and 1550 DF, p-value: 6.9397e-08
Modelos Lineales con Datos Panel Estáticos: Two-Way Fixed Effects (Implementación en R 2)
p_load ('fixest' )<- feols (lifeExp ~ log_PIBper | country + year,data = df_gapmind)summary (m1_twfe)
OLS estimation, Dep. Var.: lifeExp
Observations: 1,704
Fixed-effects: country: 142, year: 12
Standard-errors: Clustered (country)
Estimate Std. Error t value Pr(>|t|)
log_PIBper 1.44986 0.679481 2.13377 0.034592 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
RMSE: 3.26675 Adj. R2: 0.929686
Within R2: 0.018593
Modelos Lineales con Datos Panel Estáticos: Two-Way Fixed Effects
Comparación de Resultados de Modelos
library (knitr)<- data.frame (Model = c ("Efectos Fijos (FE)" , "Efectos Fijos Bidireccionales (TWFE)" ),Coefficient = c (9.769 , 1.450 ),Std_Error = c (0.297 , 0.268 ),T_Value = c (32.944 , 5.419 ),P_Value = c ("< 2.2e-16" , "6.94e-08" ),R_Squared = c (0.410 , 0.0186 ) , F = c (1085.29 , 29.3656 )kable (results_df, caption = "" )
Efectos Fijos (FE)
9.769
0.297
32.944
< 2.2e-16
0.4100
1085.2900
Efectos Fijos Bidireccionales (TWFE)
1.450
0.268
5.419
6.94e-08
0.0186
29.3656
Modelos Lineales con Datos Panel Estáticos: Two-Way Fixed Effects VS FE
¿Efectos Fijos (solo por id) vs Efectos Fijos Bidireccionales (id + tiempo)?
\[
\begin{align*}
H_0&: \beta_t = 0 \text{ (No hay efectos temporales)} \\
H_1&: \text{Al menos un } \beta_t \neq 0 \text{ (Existen efectos temporales)}
\end{align*}
\]
#FE <- plm (lifeExp ~ log_PIBper , data = df_pdata , model = "within" )#TWFE <- plm (lifeExp ~ log_PIBper, data = df_pdata, model = "within" , effect = "twoways" )print (pFtest (m_twfe , m_FE2))
F test for twoways effects
data: lifeExp ~ log_PIBper
F = 197.21, df1 = 11, df2 = 1550, p-value < 2.2e-16
alternative hypothesis: significant effects
Modelos Lineales con Datos Panel Estáticos: Two-Way Fixed Effects VS FE
Consideraciones
Tamaño muestral
Muestra pequeña
Muestra grande
Shocks
No hay shocks temporales importantes
Presencia de shocks macroeconómicos
Foco del análisis
Interés principalen variación within individual
Efectos temporales significativos
Estructura temporal
Estructura temporal simple
Necesidad de controlar tendencias temporales
Modelos Lineales con Datos Panel Estáticos: Two-Way Fixed Effects
Modelo de ecuación de salario por Two-Way Fixed Effects:
#TWFE ---- <- plm (lwage ~ union + educ + exper + I (exper^ 2 ),data = pdata_wage, model = "within" ,effect = "twoways" )summary (m_twfe_wage)
Twoways effects Within Model
Call:
plm(formula = lwage ~ union + educ + exper + I(exper^2), data = pdata_wage,
effect = "twoways", model = "within")
Balanced Panel: n = 545, T = 8, N = 4360
Residuals:
Min. 1st Qu. Median 3rd Qu. Max.
-4.162319 -0.122387 0.011382 0.156413 1.509346
Coefficients:
Estimate Std. Error t-value Pr(>|t|)
union 0.0813002 0.0193175 4.2086 2.629e-05 ***
I(exper^2) -0.0053408 0.0007023 -7.6047 3.576e-14 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Total Sum of Squares: 479.09
Residual Sum of Squares: 469.55
R-Squared: 0.019897
Adj. R-Squared: -0.12251
F-statistic: 38.633 on 2 and 3806 DF, p-value: < 2.22e-16
Modelos Lineales con Datos Panel Estáticos: Two-Way Fixed Effects
Interpretación
Estimación: 0.0813
Significancia: p < 0.001
Ser miembro de un sindicato se asocia con un aumento promedio de 8.1% en el salario dentro del mismo individuo a lo largo del tiempo.
Si observamos en la salida del modelo, no está la variable experiencia.
La variable termina siendo aproximadamente constante (muy poca variación dentro de la unidad después de ajustar por tiempo), R la elimina porque no aporta información adicional al modelo.
Modelos Lineales con Datos Panel Estáticos: Two-Way Fixed Effects
¿FE o Two-Way Fixed Effects? Prueba F para comprobar
#Modelo FE con plm ---- <- plm (lwage ~ union + educ + exper + I (exper^ 2 ) , data = pdata_wage,model = "within" , effect = 'individual' )#Efectos fijos (FE) vs Efectos fijos de dos vías (TWFE) ---- print (pFtest (m_twfe_wage , FE_plm_wage))
F test for twoways effects
data: lwage ~ union + educ + exper + I(exper^2)
F = 1.8966, df1 = 6, df2 = 3806, p-value = 0.07763
alternative hypothesis: significant effects
Modelos Lineales con Datos Panel Estáticos: Two-Way Fixed Effects
F = 1.8966 p-value ≈ 0.078 > 0.05
Conclusión: No se rechaza la hipóstesis nula al 5% de significancia. Los efectos fijos por tiempo no aportan información significativa al modelo.
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (¿Cómo funciona?)
El Estimador de diferencia en diferencias
Partimos de un modelo de efectos fijos en donde el regresor de interés es binario:
\[y_{it} = \delta_t + \alpha_i+ \phi D_{it} + c_i + u_{it}\] Donde: \[D_{it} =
\begin{cases}
1 & \text{si el individuo i recibe tratamiento/intervención en t} \\
0 & \text{en otro caso}
\end{cases}\]
Cameron & Trivedi (2005, 2009)
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (¿Cómo funciona?)
Al aplicar primeras diferencias :
\[\Delta y_{it} = (\delta_t - \delta_{t-1}) + \phi \Delta D_{it} + \Delta u_{it}\] - El efecto fijo individual desaparece.\(c_i\) y \(D_{it}\) .\(\phi\) será el efecto de tratamiento y será estimado consistentemente por pooled OLS
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (¿Cómo funciona?)
Intuición de la Primera Diferencia
Al diferenciar, estamos comparando a cada individuo consigo mismo en dos pereíodos consecutivos .
Esto elimina todo lo que es constante en el tiempo para ese individuo (ej. habilidades innatas, características estructurales, nivel socioeconómico fijo).
Solo queda la variación en el tiempo (cambio en tratamiento y shocks).
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (¿Cómo funciona?)
Considerando el caso particular de \(T = 2\) (sólo dos períodos)
Suponiendo que la intervención sólo ocurre en el período dos:
En \(t=1\) , para \(D_{i1} = 0\) para todos los \(i\)
En \(t=2\) habrá \(D_{i2} = 0\) (no tratados) y \(D_{i2} = 1\) (tratados)
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff
Por tanto el modelo a estimar en ese escenario será:
\[\Delta y_{i} = \delta + \phi D_{i} +u_{i}\]
\(D_i\) es la variable de tratamiento que indica si recibe el tratamiento o no.
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (¿Cómo funciona?)
Definiendo el promedio muestral de \(\Delta \bar y^{trat}\) y \(\Delta \bar y^{no~trat}\)
podemos definir el estimador de \(phi\) que se estima por OLS como:
\[\hat\phi= \Delta \bar y^{trat} - \Delta \bar y^{no~trat}\]
Al estimador se le conoce como estimador de diferencias-en-diferencias (DID)
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (¿Cómo funciona?)
¿Por qué Diff-in-Diff?
Primero se estima la diferencia de el grupo de tratamiento y de no tramiento en cada período y después se calcula la diferencia de esas diferencias entre cada período:
\[\hat\phi= (\bar y^{trat}_2 - \bar y^{trat}_1) - (\bar y^{no~trat}_2 - \bar y^{no~trat}_1)\]
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (¿Cómo funciona?)
Otra forma de especificar el modelo si tenemos dos grupos y dos períodos de tiempo:
\[y_i = \beta_o + \beta_1GrupoTratado_i + \beta_2 PostTrat_t + \beta_3(GrupoTratado_i*PostTrat_t) + \epsilon_i \] Donde:
\(GrupoTratado_i\) : si la unidad pertenece al grupo tratado, 0 si pertenece al grupo de contro
\(PostTrat_t\) : variable indicadora (=1 si el periodo es posterior a la introducción de la política/tratamiento, 0 en caso contrario)
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (¿Cómo funciona?)
Interpretación de coeficientes
\(\beta_0\) Valor promedio del grupo de control antes del tratamiento (baseline).
\(\beta_1\) Diferencia promedio entre el grupo tratado y el grupo de control antes del tratamiento.
\(\beta_2\) Cambio promedio en el grupo de control después del tratamiento , en comparación con el periodo previo.
\(\beta_3\) Estimador Diff-in-Diff(DID) : cuánto más (o menos) cambió el grupo tratado en comparación con el grupo de control después del tratamiento.
\(\epsilon_i\) Término de error, captura factores no observados.
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Ejemplo)
Supongamos que medimos ingresos anuales promedio antes y después de un programa.
Grupo Tratado (eligible)
Antes del tratamiento: 10,000
Después del tratamiento: 13,000
Cambio: \(\bar{y}^{tr}_2 - \bar{y}^{tr}_1 = 13,000 - 10,000 = 3,000\)
Grupo Control (no elegible)
Antes del tratamiento: 15,000
Después del tratamiento: 17,000
Cambio: \(\bar{y}^{nt}_2 - \bar{y}^{nt}_1 = 17,000 - 15,000 = 2,000\)
Efecto del tratamiento (DiD):
\(\phi = (\bar{y}^{tr}_2 - \bar{y}^{tr}_1) - (\bar{y}^{nt}_2 - \bar{y}^{nt}_1) = 3,000 - 2,000 = 1,000\)
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Ejemplo)
La diferencia adicional observada en el grupo tratado se interpreta como el efecto causal del tratamiento .
El estimador de diff-in-dif separa el efecto del tiempo \(t\) del tratamiento \(D\)
En este ejemplo: el programa aumentó los ingresos en 1,000 .
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Supuesto)
Supuesto de Tendencias Paralelas
El estimador Diff-in-Diff requiere que, en ausencia del tratamiento, la evolución media de la variable objetivo del grupo tratado, habría sido la misma que la del grupo de no tratado (control) .
\[E \big[ Y_{i,t=2}(0) \mid D_i = 1 \big] -
E \big[ Y_{i,t=1}(0) \mid D_i = 1 \big]
=
E \big[ Y_{i,t=2}(0) \mid D_i = 0 \big] -
E \big[ Y_{i,t=1}(0) \mid D_i = 0 \big]\]
El lado izquierdo: evolución esperada del grupo tratado en el escenario hipotético donde no hubieran recibido el tratamiento.
El lado derecho: evolución observada del grupo control .
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Supuesto)
¿Por qué es importante?
Este supuesto es crucial porque permite construir el contrafactual. Es decir, nos permite estimar qué habría pasado con el grupo tratado si no hubiera recibido el tratamiento.
Sin esta suposición, no podríamos aislar el impacto del tratamiento de otros factores que puedan estar afectando a ambos grupos de forma diferente.
La validez y consistencia del estimador de diff-in-diff depende por completo de que este supuesto se cumpla.
Si las tendencias de los grupos ya eran diferentes antes de la intervención, entonces las diferencias observadas después no podrían atribuirse de manera confiable al tratamiento.
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Supuesto)
¿Podemos comprobar el supuesto?
Promedio de la variable de resultado a lo largo del tiempo para ambos grupos (tratado y control). Antes de la intervención, las líneas de ambos grupos deberían seguir tendencias similares, es decir, ser aproximadamente paralelas.
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Supuesto)
Test Estadístico: Tendencias Previas (Prior Trends)
Idea: con sólo un período adicional previo \(t=0\) y \(t=1\) corre una regresión con interacción \(tratados×postpre\) .
\[y_{it} = \alpha_i + \delta postpre_t+ \lambda (GrupoTratado_i*postpre_t) +u_{it}\]
Donde:
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Supuesto)
Hipótesis
H0: el cambio medio de tratados en el pre es igual al de control, por lo tanto \(\delta = 0\) .
Si no rechazamos H0 , los tratados y controles crecieron igual en el pre, consistente con parallel trends.
El estimado de diff-in-diff podría estar sesgado
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Ejemplo aplicado)
‘Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania’ - Card & Krueger (1994)
Teoría económica estándar
Si el salario mínimo se fija por arriba del salario de equilibrio:
Resultado esperado: el salario mínimo perjudica a algunos trabajadores de bajos salarios .
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Ejemplo aplicado)
Pregunta de investigación
-¿Qué ocurre realmente con los niveles de empleos cuando sube el salario mínimo?
Contexto: Aumento del salario mínimo en Nueva Jersey
En 1991 , el salario mínimo federal en EE. UU. era $4.25/hora .
En abril de 1992 , Nueva Jersey aumentó su salario mínimo a $5.05/hora .
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Ejemplo aplicado)
Datos
Encuestaron a 410 restaurantes de comida rápida en en Nueva Jersey y en el éste de Pensilvania, antes y después de la implementación del aumento en Nueva Jersey
Utilizamos el conjunto de datos njmin de la paquetería diffindiff
#Instalación de paquetería para obtener Card & Krueger (1994): #remotes::install_github("b-rodrigues/diffindiff") p_load (diffindiff)#Datos data ("njmin" )str (njmin)
spc_tbl_ [820 × 27] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
$ sheet : chr [1:820] "46" "49" "506" "56" ...
$ chain : chr [1:820] "bk" "kfc" "kfc" "wendys" ...
$ state : chr [1:820] "Pennsylvania" "Pennsylvania" "Pennsylvania" "Pennsylvania" ...
$ region : chr [1:820] "pa1" "pa1" "pa1" "pa1" ...
$ observation: chr [1:820] "February 1992" "February 1992" "February 1992" "February 1992" ...
$ co_owned : chr [1:820] "No" "No" "Yes" "Yes" ...
$ bonus : chr [1:820] "Yes" "No" "No" "Yes" ...
$ ncalls : num [1:820] 0 0 0 0 0 2 0 0 0 2 ...
$ empft : num [1:820] 30 6.5 3 20 6 0 50 10 2 2 ...
$ emppt : num [1:820] 15 6.5 7 20 26 31 35 17 8 10 ...
$ nmgrs : num [1:820] 3 4 2 4 5 5 3 5 5 2 ...
$ wage_st : num [1:820] NA NA NA 5 5.5 5 5 5 5.25 5 ...
$ inctime : num [1:820] 19 26 13 26 52 26 26 52 13 19 ...
$ firstinc : num [1:820] NA NA 0.37 0.1 0.15 0.07 0.1 0.25 0.25 0.15 ...
$ pctaff : num [1:820] NA NA 30 0 0 45 0 0 0 0 ...
$ meals : chr [1:820] "Reduced price meals" "Reduced price meals" "Reduced price meals" "Reduced price meals" ...
$ open : num [1:820] 6.5 10 11 10 10 10 6 0 11 11 ...
$ hrsopen : num [1:820] 16.5 13 10 12 12 12 18 24 10 10 ...
$ psoda : num [1:820] 1.03 1.01 0.95 0.87 0.87 0.87 1.04 1.05 0.73 0.94 ...
$ pfry : num [1:820] 1.03 0.9 0.74 0.82 0.77 0.77 0.88 0.84 0.73 0.73 ...
$ pentree : num [1:820] 0.52 2.35 2.33 1.79 1.65 0.95 0.94 0.96 2.32 2.32 ...
$ nregs : num [1:820] 3 4 3 2 2 2 3 6 2 4 ...
$ nregs11 : num [1:820] 3 3 3 2 2 2 3 4 2 4 ...
$ type : chr [1:820] NA NA NA NA ...
$ status : chr [1:820] NA NA NA NA ...
$ date : Date[1:820], format: NA NA ...
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Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Ejemplo aplicado)
Distribución de restaurantes por estado
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Ejemplo aplicado)
Estadística Descriptiva: Participación cadenas por estado
<- njmin |> group_by ( state, chain) |> summarise (n = n ()) |> mutate (prop = n / sum (n)) |> :: select (- n) |> :: pivot_wider (names_from = state, values_from = prop, values_fill = 0 ) kable (table_dist_rest, digits = 2 , caption = "Participación en el empleo de cadenas por estados" )
Participación en el empleo de cadenas por estados
bk
0.41
0.44
kfc
0.21
0.15
roys
0.25
0.22
wendys
0.14
0.19
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Ejemplo aplicado)
Estadística Descriptiva: Medias de empleo total, porcentaje de empleo de tiempo completo, salario, horas operadas
Creación de variables:
emptot : los equivalentes de tiempo completo (FTE, por sus siglas en inglés) consisten en empleados de tiempo completo, gerentes y empleados de medio tiempo (multiplicado por 0.5)
prop_fte: proporción de empleados de tiempo completo (empft/emptot)
#Creación de variables: #emptot : los equivalentes de tiempo completo (FTE, por sus siglas en inglés) #consisten en empleados de tiempo completo, gerentes y empleados de medio tiempo (multiplicado por 0.5) . <- njmin |> mutate (emptot = empft + nmgrs + (emppt * 0.5 ), prop_fte = (empft/ emptot)* 100 )
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Ejemplo aplicado)
Medias de empleo total, porcentaje de empleo de tiempo completo, salario, horas operadas
emptot
20.44
23.33
21.03
21.17
proptaff
32.85
35.04
35.87
30.38
wage_st
4.61
4.63
5.08
4.62
hrsopen
14.42
14.53
14.42
14.65
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Ejemplo aplicado)
Primeras diferencias
\[diff_{pre} = \text{mean_tratado_pre} - \text{mean_control_pre}\]
\[diff_{post} = \text{mean_tratado_post} - \text{mean_control_post}\]
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Ejemplo aplicado)
Primeras diferencias
#Medias por grupo <- njmin |> group_by (observation, state) |> summarise (emptotal = mean (emptot , na.rm = TRUE ))# pre-tratamiento (NJ) <- mean_emptot[1 ,3 ]# pre-tratamiento (PA) Control <- mean_emptot[2 ,3 ]# post_tratamiento (NJ) <- mean_emptot[3 ,3 ]# post_tratamiento (PA) Control <- mean_emptot[4 ,3 ]#Diferencia de grupo tratado vs control pre <- mean_njfeb - mean_pafeb #Diferencia de grupo tratado vs control post <- mean_njnov - mean_panovprint (diff_pre)
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Ejemplo aplicado)
Segunda diferencia
\[ATE = diff_{post} - diff_{pre}\]
#Diferencia de grupo tratado vs control pre <- mean_njfeb - mean_pafeb #Diferencia de grupo tratado vs control post <- mean_njnov - mean_panov#ATE <- diff_post - diff_pre print (ATE)
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Ejemplo aplicado)
Interpretación del efecto promedio de tratamiento (ATE):
“El aumento del salario mínimo en Nueva Jersey se asoció con un incremento promedio de aproximadamente 2.76 empleados de tiempo completo equivalente por restaurante de comida rápida, en comparación con los restaurantes similares en Pensilvania.”
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Ejemplo aplicado: Estimación)
Estimación por Diferencias-en-Diferencias
Método de interacción por OLS
#1. Es necesario crear las variables dummy's de tratamiento (GrupoTratado_i) y tiempo (PostTrat_t) ---- <- njmin |> mutate (PostTrat = ifelse (observation == "November 1992" , 1 , 0 ),GrupoTratado = ifelse (state == "New Jersey" , 1 , 0 ) )<- lm (emptot ~ PostTrat + GrupoTratado + PostTrat: GrupoTratado,data = njmin)summary (model_did_inter)
Call:
lm(formula = emptot ~ PostTrat + GrupoTratado + PostTrat:GrupoTratado,
data = njmin)
Residuals:
Min 1Q Median 3Q Max
-21.166 -6.439 -1.027 4.473 64.561
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 23.331 1.072 21.767 <2e-16 ***
PostTrat -2.166 1.516 -1.429 0.1535
GrupoTratado -2.892 1.194 -2.423 0.0156 *
PostTrat:GrupoTratado 2.754 1.688 1.631 0.1033
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 9.406 on 790 degrees of freedom
(26 observations deleted due to missingness)
Multiple R-squared: 0.007401, Adjusted R-squared: 0.003632
F-statistic: 1.964 on 3 and 790 DF, p-value: 0.118
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Ejemplo aplicado: Estimación)
Estimación por Diferencias-en-Diferencias
Método Efectos Fijos (TWFE)
#Recordando: Le damos estructura de panel al df p_load ('plm' )<- pdata.frame (njmin, index = c ("sheet" ,"PostTrat" ))#Model TWFE <- plm ( emptot ~ GrupoTratado* PostTrat,data = df_panel_njmin,model = "within" , # efectos fijos de unidad effect = "twoways" ) # también efectos fijos de tiempo summary (model_did_inter)
Call:
lm(formula = emptot ~ PostTrat + GrupoTratado + PostTrat:GrupoTratado,
data = njmin)
Residuals:
Min 1Q Median 3Q Max
-21.166 -6.439 -1.027 4.473 64.561
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 23.331 1.072 21.767 <2e-16 ***
PostTrat -2.166 1.516 -1.429 0.1535
GrupoTratado -2.892 1.194 -2.423 0.0156 *
PostTrat:GrupoTratado 2.754 1.688 1.631 0.1033
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 9.406 on 790 degrees of freedom
(26 observations deleted due to missingness)
Multiple R-squared: 0.007401, Adjusted R-squared: 0.003632
F-statistic: 1.964 on 3 and 790 DF, p-value: 0.118
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Ejemplo aplicado: Estimación)
Interpretación
“El aumento en el salario mínimo está asociado con un incremento promedio 2.754 de empleados de tiempos completo en Nueva Jersey, en comparación de Pensilvania.”
Importante : el efecto no es estadísticamente significativo al 5% (p = 0.1033). Es marginalmente significativo al 10%.
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Críticas)
¿Qué tan válidos son estos resultados
Recordemos que el principal suspuesto es el de tendencias pararelas , el nivel de empleo tendría que ser en promedio el mismo en los dos grupos en ausencia del tratamiento.
El estudio original no tenía datos para períodos adicionales así que realizaron un revisión (2000) en donde obtuvieron datos administrativos de nómina de restaurantes de Nueva Jersey y Pensilvania.
Al igual en los datos originales se muestra un ligero descenso del empleo en Pensilvania entre febrero y noviembre de 1992, y poco cambio en Nueva Jersey durante el mismo período.
Sin embargo, los datos también revelan variaciones considerables en el empleo de un año a otro en otros períodos. Pennsylvania ya tenía una tendencia diferente a New Jersey antes del aumento del salario mínimo.
Esto sugirió que Pensilvania podría no ser un buen contrafactual para estimar el empleo que habría tenido Nueva Jersey en ausencia de la política, y viceversa.
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Historia)
Orígenes históricos: John Snow y el cólera
En 1854, John Snow realizó uno de los primeros análisis comparativos en salud pública.
Estudió el brote de cólera en Londres , comparando tasas de mortalidad entre diferentes barrios antes y después de cerrar la bomba de agua contaminada.
Este análisis puede considerarse un antecedente temprano del DID , al comparar grupos tratados y no tratados en distintos periodos de tiempo.
El mapa de cólera de John Snow
Modelos Lineales con Datos Panel Estáticos: Diff-in-Diff (Historia)
Formalización moderna del DID
El método DID se formalizó econométricamente en los años 70-80.
Ashenfelter (1978):Using the Longitudinal Structure of Earnings to Estimate the Effect of Training Programs .
Orley Ashenfelter;David Card (1985): Using the Longitudinal Structure of Earnings to Estimate the Effect of Training Programs
Estimaron los efectos de programas de capacitación laboral usando diferencias antes/después y grupo de control.
Desde entonces, DID se ha convertido en herramienta clave para evaluación de políticas públicas y análisis causal con datos de panel .
Modelos Lineales con Datos Panel Estáticos: Random Effects
Recordemos nuestro efecto no observado (efecto constante individual no observado): \(c_i\)
En FE el objetivo er eliminar \(c_i\) con el método demeaned (extracción de la media), ya que pensamos que los \(c_i\) están correlacionado con \(x_{it}\) .
Discusión: ¿Tratar como variable aleatoría o como un parámetro con el que tenemos que estimar?
\[Cov(\mathbf{x_{it},c_i}) =0,~~~t = 1,2,...,T \] #### Modelos Lineales con Datos Panel Estáticos: Random Effects {.smaller}
Tenemos un supuesto de media condicional más fuerte:
\[E(c_i |\mathbf{x_{i1}},...,\mathbf{x_{iT}}) = E(c_{i}) = 0\]
En FE, cuando controlamos por el efecto fijo individual permitimos cierta correlación de \(c_{i}\) con \(x_{it}\) . si no están correlacionados y tratamos de controlar el efecto individual obtendremos un estimador ineficiente.
Modelos Lineales con Datos Panel
Random Effects (Estimación)¿Cómo podemos estimar \(\beta\) cuando pensemos que se cumple que \(c_{i}\) y \(x_{it}\) no estén correlacionadas?
Podríamos utilizar POLS y obtendríamos un estimador consistente PERO ignoramos la correlación serial de \({v}_{it}\)
\[{v}_{it} = {c}_{i} + {u}_{it} \]
Como \({c}_{i}\) está presente en todos los períodos de tiempo:
\[Cov({v}_{it},v_{is}) = \frac{\sigma_{c}^2}{\sigma_{c}^2 +\sigma_{u}^2 } \]
Un método que utilizamos para estimar modelos cuando existe autocorrelación serial es el de Mínimo Cuadrados Generalizados (GLS).
Modelos Lineales con Datos Panel: Random Effects (Estimación)
Recordemos que el método de FE sólo permite la variación within, pero si tenemos pocas observaciones los efectos fijos inviduales estarán sesgados \(\beta_{i}s\) , y por lo tanto \(\hat\beta_{FE}\) también.
El método de RE hará supuestos de la distribución del efecto fijo individual \(\beta_{i}s\) , tratando de solucionar la correlación serial del error compuesto \(v_i\) y asignándole una estructura “especial” a los errores idiosincráticos .
\(\therefore\) estimamos en un marco de Mínimos Cuadrados Generalizados (GLS)
Modelos Lineales con Datos Panel: Random Effects (Estimación)
A tráves del framework de Mínimo Cuadrados Generalizados (GLS ) el enfoque de RE explota la correlación serial.
Para que la estimación sea consistente necesitamos estricta exogeneidad entre las variables explicativas y el error compuesto
Modelos Lineales con Datos Panel: Random Effects (Estimación)
¿Qué modelo estimaremos?
\[ \textbf{y}_{i}= \textbf{X}_{i}\boldsymbol{\beta} + \textbf{v}_{i} ~~~t=1,2,...T\]
Modelos Lineales con Datos Panel: Random Effects (Estimación)
El error compuesto se escribe como:
\(\textbf{v}_{i} = c_i* \textbf{j}{T} + \textbf{u}_{i}\)
Donde:
\(\textbf{v}_{i}\) : es un vector de \(T\) X 1 de errores compuestos
\(c_{i}\) : es el efecto individual no observado
\(\textbf{j}_{T}\) : es un vector de unos
\(\textbf{u}_{i}\) : vector de errores idiosincráticos
Modelos Lineales con Datos Panel: Random Effects (Supuestos)
RE.1 Exogeneidad estricta :
\(a) E(u_{it}|\mathbf{x_{i}},c_i) = 0 ,~~t=1,...,T\)
\(b) E(c_{i}| \mathbf{x_{i}}) = E(c_{i})=0\)
\(where~~ \mathbf{x_{i}}\equiv(\mathbf{x_{i1}},\mathbf{x_{i2}},...,\mathbf{x_{iT}})\)
Modelos Lineales con Datos Panel: Random Effects (Supuestos)
Tendremos una matriz de varianzas incondicionales de \(\textbf{v}_{i}\) :
\[ \Omega \equiv \mathbb{E}(\textbf{v}_i \textbf{v}_i')\] - Es decir la matriz de varianzas y covarianza
Modelos Lineales con Datos Panel: Random Effects (Supuestos)
Debemos de suponer que la matriz de varianzas-covarianzas es definida positiva, significa:
Esto garantiza que no haya colinealidad perfecta ni combinaciones lineales triviales entre los errores.
Así, la matriz puede invertirse, asi obtendremos estimadores consistentes de Mínimos Cuadrados Generalizados (GLS).
Por tanto:
\[rank E( \mathbf{X_{i}}' \Omega^{-1} \mathbf{X_{i}})] = K\]
Modelos Lineales con Datos Panel: Random Effects (Supuestos)
Con la matriz \(\Omega\) le daremos estructura a los errores idiosincráticos y por tanto se tienen que cumplir los supuestos:
Varianza constante incondicional: \(E(u_{it}^2) = \sigma^2_{u}\)
Errors idiosincráticos son serialmente no correlacionados:\(~~E(u_{it}, u_{is}) = 0 ~~t\neq s\)
Modelos Lineales con Datos Panel: Random Effects (Supuestos)
Bajo esos supuestos podemos calcular las varianzas y covarianzas de \(\textbf{v}_{i}\)
Tomando en cuenta que RE.1 \(E(c_{i}u_{it}) = 0,~~t=1,2,...T\) la varianza será:
\[ E(v_{it}^2) = E(c_{i}^2) + E(u_{it}^2) + 2E(c_{i}^2u_{it}^2) = \sigma^2_{c} + \sigma^2_{u} \]
Modelos Lineales con Datos Panel: Random Effects (Supuestos)
Para la covarianza :
\[E(v_{it}v_{is}) = E[(c\_{i} + u_{it}))(c_{i}+u_{is}))]\]
\[= E(c_i^2) + E(c_iu_{is}) + E(u_{it}c_i) + E(u_{it}u_{is}) \]
Dados los supuestos RE.1 y \(~~E(u_{it}, u_{is}) = 0\)
\[\therefore ~~ E(v_{it}v_{is}) = \sigma^2_{c}\]
Modelos Lineales con Datos Panel:Random Effects (Supuestos)
La matriz \(\Omega\) tomará la siguiente forma especial: efectos aleatorios .
\[\Omega = \mathbb{E}(v_i v_i') = \begin{pmatrix}
\sigma_c^2 + \sigma_u^2 & \sigma_c^2 & \cdots & \sigma_c^2 \\
\sigma_c^2 & \sigma_c^2 + \sigma_u^2 & \cdots & \sigma_c^2 \\
\vdots & \vdots & \ddots & \vdots \\
\sigma_c^2 & \sigma_c^2 & \cdots & \sigma_c^2 + \sigma_u^2
\end{pmatrix}\]
También podemos representar la matriz de esta forma:
\(\Omega= \sigma_{u} ^2\mathbf{I_{T}}+\sigma^2_{c}\mathbf{j_{T}}\mathbf{j'_{T}}\)
Modelos Lineales con Datos Panel: Random Effects (Supuestos)
RE.3 Homocedasticidad :
\[ a) E(u_{it}^2|\mathbf{x_{i}},c_i) = \sigma^2_{u}\mathbf{I}_T \]
\[b) E(c^2_{i}|\mathbf{x_{i}}) = \sigma^2_{c}\]
Más estricto porque asume que la varianza condicional es constante y las covarianzas son cero.
Varianza condicional del efecto no observado con las variables es constante.
Se mantiene la forma de \(\Omega\)
No correlación serial entre \(c_i\) y \(\mathbf{x_{it}}\)
Modelos Lineales con Datos Panel:Random Effects (Supuestos)
Como no conocemos \(\Omega\) , tenemos que estimarla:
\[\hat\Omega= \hat\sigma_{u} ^2\mathbf{I_{T}}+\hat\sigma^2_{c}\mathbf{j_{T}}\mathbf{j'_{T}}\]
Obtenemos los residuales del modelo POLS para estimar \(\sigma^2_{v}\) :
\[ \hat\sigma_v^2 = \frac{1}{NT-K} \sum_{i=1}^N \sum_{t=1}^T \hat{\hat{v}} _{it}^2\] Donde: \(NT-K\) es la corrección por grados de libertad
Modelos Lineales con Datos Panel:Random Effects (Supuestos)
Para obtener un estimador de \(\sigma^2_{c}\) recordamos que \(\sigma^2_{c} = E(v_{it}v_{is})\) :
\[\hat\sigma_c^2 = \frac{1}{[NT(T-1)/2-K]} \sum_{i=1}^N \sum_{t=1}^{T-1} \sum_{s=t+1}^T \hat{\hat{v}}_{it} \hat{\hat{v}}_{is}\] Donde: \(NT(T-1)/2-K\) es la corrección por grados de libertad
Modelos Lineales con Datos Panel:Random Effects (Supuestos)
Dado que estimamos \(\hat\sigma_v^2\) y \(\hat\sigma_c^2\) podemos estimar:
\[\hat\sigma_u^2 = \hat\sigma_v^2 - \hat\sigma_c^2\]
Modelos Lineales con Datos Panel
Random Effects (Estimación)El estimador de Efectos Aleatorios (RE) se representa como:
\[
\therefore~~~~~\hat{\beta}_{RE} = \left( \sum_{i=1}^{N} \mathbf{x_i}' \hat{\Omega}^{-1} \mathbf{x_i} \right)^{-1} \left( \sum_{i=1}^{N} \mathbf{x_i}' \hat{\Omega}^{-1} \mathbf{y_i} \right)
\]
Modelos Lineales con Datos Panel
Random Effects (Ventajas y desventajas)
Por la estructura impuesta a los errores podemos tener estimaciones más precisas, es decir, errores estándares más bajos.
Mejora la estimación de los errores fijos individuales (\(\beta_{i}s\) )
En lugar de sólo utilizar la variación within, implementa una ponderación entre la variación between y within.
Necesitamos que \(\beta_{i}s\) no estén relacionadas con las variables explicativas.
Ejemplo: ¿Efectos fijos individuales de cada país está relacionado con el PIB percapita?
Modelos Lineales con Datos Panel
Efectos aleatorios (RE) vs Efectos Fijos (FE)
Variabilidad entre unidades
Absorbida por efectos específicos
Tratada como aleatoria
Efectos no observados
Correlacionados con las variables explicativa
No correlacionados con las variables
Estimación de variables que no cambian en el tiempo
No posible
Posible
Uso de variabilidad
Within
Ponderación within y between
Modelos Lineales con Datos Panel
Efectos aleatorios (RE) vs Efectos Fijos (FE)
FE permite correlación serial entre \(c_i\) y \(\mathbf{x_{it}}\) y RE no.
FE es un método más utilizado porque dificilmente \(\beta_{i}s\) y \(\mathbf{x_{it}}\) no estarán correlacionados.
En RE se utilizan más variables explicativas que son constantes en el tiempo, respecto a FE.
RE nos da estimador más eficiente
Si las unidades de observación son extensiones geográficas grandes (estados, países o provincias) utilizamos FE.
La cuestión clave para determina si usamos FE o RE, es si pertinentemente podemos asumir que \(c_i\) no está correlacionado con \(\mathbf{x_{it}}\) .
Modelos Lineales con Datos Panel
RE vs FE (Implementación en R)
#Convertimos panel df <- pdata.frame (df_gapmind , index = c ("country" , "year" ))#Estimación por FE <- plm (lifeExp ~ log_PIBper , data = df_pdata , model = "within" , effect = 'individual' )#Estimación por RE <- plm (lifeExp ~ log_PIBper , data = df_pdata , model = "random" )summary (m_RE)
Oneway (individual) effect Random Effect Model
(Swamy-Arora's transformation)
Call:
plm(formula = lifeExp ~ log_PIBper, data = df_pdata, model = "random")
Balanced Panel: n = 142, T = 12, N = 1704
Effects:
var std.dev share
idiosyncratic 27.953 5.287 0.481
individual 30.114 5.488 0.519
theta: 0.732
Residuals:
Min. 1st Qu. Median 3rd Qu. Max.
-23.62988 -2.69970 0.25631 3.20672 16.05044
Coefficients:
Estimate Std. Error z-value Pr(>|z|)
(Intercept) -15.89278 2.02424 -7.8512 4.12e-15 ***
log_PIBper 9.23755 0.24105 38.3214 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Total Sum of Squares: 89063
Residual Sum of Squares: 47811
R-Squared: 0.46318
Adj. R-Squared: 0.46287
Chisq: 1468.53 on 1 DF, p-value: < 2.22e-16
Modelos Lineales con Datos Panel
RE vs FE (Interpretación de Resultados)
Varianzas y Efectos:
Idiosincrático: La varianza idiosincrática es 27.953 con una desviación estándar de 5.287, lo que indica que la variabilidad en los residuos que no puede explicarse por las variables independientes utilizadas es alta.
Individual: La varianza individual es 30.114 con una desviación estándar de 5.488, sugiere que la variabilidad entre países es importante y por tanto el PIB per capita no se asocia de de forma uniforme con la esperanza de vida entre los distintos países.
Proporción: La proporción de la varianza idiosincrática es 48.1% y la varianza individual es 51.9%, lo que indica que la variabilidad entre individuos (países) y la variabilidad idiosincrática son aproximadamente iguales en su contribución al total de la varianza.
El valor de \(\theta\) = 0.732 sugiere que una proporción considerable de la variabilidad en la esperanza de vida puede ser explicada por efectos no observables individualea de los países. Factor de transformación.
Modelos Lineales con Datos Panel
RE vs FE (Hausman Test)
\[
\begin{align*}
H_0&: \text{Cov}(x_{it}, c_i) = 0 \text{ (Efectos Aleatorios es consistente y eficiente)} \\
H_1&: \text{Cov}(x_{it}, c_i) \neq 0 \text{ (Efectos Fijos es consistente)}
\end{align*}
\]
\[
H = (β_{FE} - β_{RE})'[Var(β_{FE}) - Var(β_{RE})]^{-1}(β_{FE} - β_{RE}) \sim \chi^2_k
\]
Modelos Lineales con Datos Panel
RE vs FE (Hausman Test en R)
# Test de Hausman phtest (m_FE2, m_RE)
Hausman Test
data: lifeExp ~ log_PIBper
chisq = 9.4684, df = 1, p-value = 0.00209
alternative hypothesis: one model is inconsistent
Los resultados de la prueba de Hausman indican que el modelo de efectos fijos es consistente.
Modelos Lineales con Datos Panel
RE vs POLS (Test Lagrange Multiplier (LM) de Breusch-Pagan )
# Modelo pooled (OLS) <- plm (lifeExp ~ log_PIBper, data = df_pdata, model = "pooling" )# Modelo de efectos aleatorios <- plm (lifeExp ~ log_PIBper, data = df_pdata, model = "random" )plmtest (pooled_plm, type = "bp" )
Lagrange Multiplier Test - (Breusch-Pagan)
data: lifeExp ~ log_PIBper
chisq = 2454.3, df = 1, p-value < 2.2e-16
alternative hypothesis: significant effects
